Algorithms
http://www.mdpi.com/journal/algorithms
Latest open access articles published in Algorithms at http://www.mdpi.com/journal/algorithms<![CDATA[Algorithms, Vol. 9, Pages 37: A New Multi-Step Iterative Algorithm for Approximating Common Fixed Points of a Finite Family of Multi-Valued Bregman Relatively Nonexpansive Mappings]]>
http://www.mdpi.com/1999-4893/9/2/37
In this article, we introduce a new multi-step iteration for approximating a common fixed point of a finite class of multi-valued Bregman relatively nonexpansive mappings in the setting of reflexive Banach spaces. We prove a strong convergence theorem for the proposed iterative algorithm under certain hypotheses. Additionally, we also use our results for the solution of variational inequality problems and to find the zero points of maximal monotone operators. The theorems furnished in this work are new and well-established and generalize many well-known recent research works in this field.Algorithms2016-05-3092Article10.3390/a9020037371999-48932016-05-30doi: 10.3390/a9020037Wiyada KumamPongsakorn SunthrayuthPhond PhunchongharnKhajonpong AkkarajitsakulParinya NgiamsunthornPoom Kumam<![CDATA[Algorithms, Vol. 9, Pages 36: Robust Hessian Locally Linear Embedding Techniques for High-Dimensional Data]]>
http://www.mdpi.com/1999-4893/9/2/36
Recently manifold learning has received extensive interest in the community of pattern recognition. Despite their appealing properties, most manifold learning algorithms are not robust in practical applications. In this paper, we address this problem in the context of the Hessian locally linear embedding (HLLE) algorithm and propose a more robust method, called RHLLE, which aims to be robust against both outliers and noise in the data. Specifically, we first propose a fast outlier detection method for high-dimensional datasets. Then, we employ a local smoothing method to reduce noise. Furthermore, we reformulate the original HLLE algorithm by using the truncation function from differentiable manifolds. In the reformulated framework, we explicitly introduce a weighted global functional to further reduce the undesirable effect of outliers and noise on the embedding result. Experiments on synthetic as well as real datasets demonstrate the effectiveness of our proposed algorithm.Algorithms2016-05-2692Article10.3390/a9020036361999-48932016-05-26doi: 10.3390/a9020036Xianglei XingSidan DuKejun Wang<![CDATA[Algorithms, Vol. 9, Pages 35: Application of the Energy-Conserving Integration Method to Hybrid Simulation of a Full-Scale Steel Frame]]>
http://www.mdpi.com/1999-4893/9/2/35
The nonlinear unconditionally stable energy-conserving integration method (ECM) is a new method for solving a continuous equation of motion. To our knowledge, there is still no report about its application on a hybrid test. Aiming to explore its effect on hybrid tests, the nonlinear beam-column element program is developed for computation. The program contains both the ECM and the average acceleration method (AAM). The comparison of the hybrid test results with thesetwo methods validates the effectiveness of the ECM in the hybrid simulation. We found that the energy error of hybrid test by using ECM is less than that of AAM. In addition, a new iteration strategy with reduction factor is presented to avoid the overshooting phenomena during iteration process with the finite element program.Algorithms2016-05-2192Article10.3390/a9020035351999-48932016-05-21doi: 10.3390/a9020035Tianlin PanBin WuYongsheng ChenGuoshan Xu<![CDATA[Algorithms, Vol. 9, Pages 34: A State Recognition Approach for Complex Equipment Based on a Fuzzy Probabilistic Neural Network]]>
http://www.mdpi.com/1999-4893/9/2/34
Due to the traditional state recognition approaches for complex electromechanical equipment having had the disadvantages of excessive reliance on complete expert knowledge and insufficient training sets, real-time state identification system was always difficult to be established. The running efficiency cannot be guaranteed and the fault rate cannot be reduced fundamentally especially in some extreme working conditions. To solve these problems, an online state recognition method for complex equipment based on a fuzzy probabilistic neural network (FPNN) was proposed in this paper. The fuzzy rule base for complex equipment was established and a multi-level state space model was constructed. Moreover, a probabilistic neural network (PNN) was applied in state recognition, and the fuzzy functions and quantification matrix were presented. The flowchart of proposed approach was designed. Finally, a simulation example of shearer state recognition and the industrial application with an accuracy of 90.91% were provided and the proposed approach was feasible and efficient.Algorithms2016-05-2092Article10.3390/a9020034341999-48932016-05-20doi: 10.3390/a9020034Jing XuZhongbin WangChao TanXinhua Liu<![CDATA[Algorithms, Vol. 9, Pages 33: Mining Branching Rules from Past Survey Data with an Illustration Using a Geriatric Assessment Survey for Older Adults with Cancer]]>
http://www.mdpi.com/1999-4893/9/2/33
We construct a fast data mining algorithm that can be used to identify high-frequency response patterns in historical surveys. Identification of these patterns leads to the derivation of question branching rules that shorten the time required to complete a survey. The data mining algorithm allows the user to control the error rate that is incurred through the use of implied answers that go along with each branching rule. The context considered is binary response questions, which can be obtained from multi-level response questions through dichotomization. The algorithm is illustrated by the analysis of four sections of a geriatric assessment survey used by oncologists. Reductions in the number of questions that need to be asked in these four sections range from 33% to 54%.Algorithms2016-05-1392Article10.3390/a9020033331999-48932016-05-13doi: 10.3390/a9020033Daniel JeskeJeffrey LongmateVani KatheriaArti Hurria<![CDATA[Algorithms, Vol. 9, Pages 32: Uniform vs. Nonuniform Membership for Mildly Context-Sensitive Languages: A Brief Survey]]>
http://www.mdpi.com/1999-4893/9/2/32
Parsing for mildly context-sensitive language formalisms is an important area within natural language processing. While the complexity of the parsing problem for some such formalisms is known to be polynomial, this is not the case for all of them. This article presents a series of results regarding the complexity of parsing for linear context-free rewriting systems and deterministic tree-walking transducers. We discuss the difference between uniform and nonuniform complexity measures and how parameterized complexity theory can be used to investigate how different aspects of the formalisms influence how hard the parsing problem is. The main results we survey are all hardness results and indicate that parsing is hard even for relatively small values of parameters such as rank and fan-out in a rewriting system.Algorithms2016-05-1192Article10.3390/a9020032321999-48932016-05-11doi: 10.3390/a9020032Henrik BjörklundMartin BerglundPetter Ericson<![CDATA[Algorithms, Vol. 9, Pages 31: Improved Direct Linear Transformation for Parameter Decoupling in Camera Calibration]]>
http://www.mdpi.com/1999-4893/9/2/31
For camera calibration based on direct linear transformation (DLT), the camera’s intrinsic and extrinsic parameters are simultaneously calibrated, which may cause coupling errors in the parameters and affect the calibration parameter accuracy. In this paper, we propose an improved direct linear transformation (IDLT) algorithm for calibration parameter decoupling. This algorithm uses a linear relationship of calibration parameter errors and obtains calibration parameters by moving a three-dimensional template. Simulation experiments were conducted to compare the calibration accuracy of DLT and IDLT algorithms with image noise and distortion. The results show that the IDLT algorithm calibration parameters achieve higher accuracy because the algorithm removes the coupling errors.Algorithms2016-04-2992Article10.3390/a9020031311999-48932016-04-29doi: 10.3390/a9020031Zhenqing ZhaoDong YeXin ZhangGang ChenBin Zhang<![CDATA[Algorithms, Vol. 9, Pages 30: Comment on: On the Kung-Traub Conjecture for Iterative Methods for Solving Quadratic Equations. Algorithms 2016, 9, 1]]>
http://www.mdpi.com/1999-4893/9/2/30
Kung-Traub conjecture states that an iterative method without memory for finding the simple zero of a scalar equation could achieve convergence order 2 d − 1 , and d is the total number of function evaluations. In an article “Babajee, D.K.R. On the Kung-Traub Conjecture for Iterative Methods for Solving Quadratic Equations, Algorithms 2016, 9, 1, doi:10.3390/a9010001”, the author has shown that Kung-Traub conjecture is not valid for the quadratic equation and proposed an iterative method for the scalar and vector quadratic equations. In this comment, we have shown that we first reported the aforementioned iterative method.Algorithms2016-04-2692Comment10.3390/a9020030301999-48932016-04-26doi: 10.3390/a9020030Fayyaz Ahmad<![CDATA[Algorithms, Vol. 9, Pages 29: An Improved Dynamic Joint Resource Allocation Algorithm Based on SFR]]>
http://www.mdpi.com/1999-4893/9/2/29
Inter-cell interference (ICI) is the main factor affecting system capacity and spectral efficiency. Effective spectrum resource management is an important and challenging issue for the design of wireless communication systems. The soft frequency reuse (SFR) is regarded as an interesting approach to significantly eliminate ICI. However, the allocation of resource is fixed prior to system deployment in static SFR. To overcome this drawback, this paper adopts a distributed method and proposes an improved dynamic joint resource allocation algorithm (DJRA). The improved scheme adaptively adjusts resource allocation based on the real-time user distribution. DJRA first detects the edge-user distribution vector to determine the optimal scheme, which guarantees that all the users have available resources and the number of iterations is reduced. Then, the DJRA maximizes the throughput for each cell via optimizing resource and power allocation. Due to further eliminate interference, the sector partition method is used in the center region and in view of fairness among users, the novel approach adds the proportional fair algorithm at the end of DJRA. Simulation results show that the proposed algorithm outperforms previous approaches for improving the system capacity and cell edge user performance.Algorithms2016-04-2292Article10.3390/a9020029291999-48932016-04-22doi: 10.3390/a9020029Yibing LiXueying DiaoGe DongFang Ye<![CDATA[Algorithms, Vol. 9, Pages 28: Alternating Direction Method of Multipliers for Generalized Low-Rank Tensor Recovery]]>
http://www.mdpi.com/1999-4893/9/2/28
Low-Rank Tensor Recovery (LRTR), the higher order generalization of Low-Rank Matrix Recovery (LRMR), is especially suitable for analyzing multi-linear data with gross corruptions, outliers and missing values, and it attracts broad attention in the fields of computer vision, machine learning and data mining. This paper considers a generalized model of LRTR and attempts to recover simultaneously the low-rank, the sparse, and the small disturbance components from partial entries of a given data tensor. Specifically, we first describe generalized LRTR as a tensor nuclear norm optimization problem that minimizes a weighted combination of the tensor nuclear norm, the l1-norm and the Frobenius norm under linear constraints. Then, the technique of Alternating Direction Method of Multipliers (ADMM) is employed to solve the proposed minimization problem. Next, we discuss the weak convergence of the proposed iterative algorithm. Finally, experimental results on synthetic and real-world datasets validate the efficiency and effectiveness of the proposed method.Algorithms2016-04-1992Article10.3390/a9020028281999-48932016-04-19doi: 10.3390/a9020028Jiarong ShiQingyan YinXiuyun ZhengWei Yang<![CDATA[Algorithms, Vol. 9, Pages 27: The Effect of Preprocessing on Arabic Document Categorization]]>
http://www.mdpi.com/1999-4893/9/2/27
Preprocessing is one of the main components in a conventional document categorization (DC) framework. This paper aims to highlight the effect of preprocessing tasks on the efficiency of the Arabic DC system. In this study, three classification techniques are used, namely, naive Bayes (NB), k-nearest neighbor (KNN), and support vector machine (SVM). Experimental analysis on Arabic datasets reveals that preprocessing techniques have a significant impact on the classification accuracy, especially with complicated morphological structure of the Arabic language. Choosing appropriate combinations of preprocessing tasks provides significant improvement on the accuracy of document categorization depending on the feature size and classification techniques. Findings of this study show that the SVM technique has outperformed the KNN and NB techniques. The SVM technique achieved 96.74% micro-F1 value by using the combination of normalization and stemming as preprocessing tasks.Algorithms2016-04-1892Article10.3390/a9020027271999-48932016-04-18doi: 10.3390/a9020027Abdullah AyedhGuanzheng TANKhaled AlwesabiHamdi Rajeh<![CDATA[Algorithms, Vol. 9, Pages 26: siEDM: An Efficient String Index and Search Algorithm for Edit Distance with Moves]]>
http://www.mdpi.com/1999-4893/9/2/26
Although several self-indexes for highly repetitive text collections exist, developing an index and search algorithm with editing operations remains a challenge. Edit distance with moves (EDM) is a string-to-string distance measure that includes substring moves in addition to ordinal editing operations to turn one string into another. Although the problem of computing EDM is intractable, it has a wide range of potential applications, especially in approximate string retrieval. Despite the importance of computing EDM, there has been no efficient method for indexing and searching large text collections based on the EDM measure. We propose the first algorithm, named string index for edit distance with moves (siEDM), for indexing and searching strings with EDM. The siEDM algorithm builds an index structure by leveraging the idea behind the edit sensitive parsing (ESP), an efficient algorithm enabling approximately computing EDM with guarantees of upper and lower bounds for the exact EDM. siEDM efficiently prunes the space for searching query strings by the proposed method, which enables fast query searches with the same guarantee as ESP. We experimentally tested the ability of siEDM to index and search strings on benchmark datasets, and we showed siEDM’s efficiency.Algorithms2016-04-1592Article10.3390/a9020026261999-48932016-04-15doi: 10.3390/a9020026Yoshimasa TakabatakeKenta NakashimaTetsuji KuboyamaYasuo TabeiHiroshi Sakamoto<![CDATA[Algorithms, Vol. 9, Pages 25: Primary User Localization Algorithm Based on Compressive Sensing in Cognitive Radio Networks]]>
http://www.mdpi.com/1999-4893/9/2/25
In order to locate source signal more accurately in authorized frequency bands, a novel primary user localization algorithm based on compressive sensing (PU-CSL) in cognitive radio networks (CRNs) is proposed in this paper. In comparison to existing centroid locating algorithms, PU-CSL shows higher locating accuracy for integrally exploring correlation between source signal and secondary users (SUs). Energy detection is first adopted for collecting the energy fingerprint of source signal at each SU, then degree of correlation between source signal and SUs is reconstructed based on compressive sensing (CS), which determines weights of centroid coordinates. A weighted centroid scheme is finally utilized to estimate source position. Simulation results show that PU-CSL has smaller maximum error of positioning and root-mean-square error. Moreover, the proposed PU-CSL algorithm possess excellent location accuracy and strong anti-noise performance.Algorithms2016-04-1492Article10.3390/a9020025251999-48932016-04-14doi: 10.3390/a9020025Fang YeXun ZhangYibing LiHui Huang<![CDATA[Algorithms, Vol. 9, Pages 24: Structural Damage Localization by the Principal Eigenvector of Modal Flexibility Change]]>
http://www.mdpi.com/1999-4893/9/2/24
Using the principal eigenvector (PE) of modal flexibility change, a new vibration-based algorithm for structural defect localization was presented in this paper. From theoretical investigations, it was proven that the PE of modal flexibility variation has a turning point with a sharp peak in its curvature at the damage location. A three-span continuous beam was used as an example to illustrate the feasibility and superiority of the proposed PE algorithm for damage localization. Furthermore, defect localization was also performed using the well-known uniform load surface approach for comparison. Numerical results demonstrated that the PE algorithm can locate structural defects with good accuracy, whereas the ULS approach occasionally missed one or two defect locations. It was found that the PE algorithm may be promising for structural defect assessment.Algorithms2016-04-1392Article10.3390/a9020024241999-48932016-04-13doi: 10.3390/a9020024Cui-Hong LiQiu-Wei YangBing-Xiang Sun<![CDATA[Algorithms, Vol. 9, Pages 23: An Improved Fireworks Algorithm Based on Grouping Strategy of the Shuffled Frog Leaping Algorithm to Solve Function Optimization Problems]]>
http://www.mdpi.com/1999-4893/9/2/23
The fireworks algorithm (FA) is a new parallel diffuse optimization algorithm to simulate the fireworks explosion phenomenon, which realizes the balance between global exploration and local searching by means of adjusting the explosion mode of fireworks bombs. By introducing the grouping strategy of the shuffled frog leaping algorithm (SFLA), an improved FA-SFLA hybrid algorithm is put forward, which can effectively make the FA jump out of the local optimum and accelerate the global search ability. The simulation results show that the hybrid algorithm greatly improves the accuracy and convergence velocity for solving the function optimization problems.Algorithms2016-04-0192Article10.3390/a9020023231999-48932016-04-01doi: 10.3390/a9020023Yu-Feng SunJie-Sheng WangJiang-Di Song<![CDATA[Algorithms, Vol. 9, Pages 22: Modifying Orthogonal Drawings for Label Placement]]>
http://www.mdpi.com/1999-4893/9/2/22
In this paper, we investigate how one can modify an orthogonal graph drawing to accommodate the placement of overlap-free labels with the minimum cost (i.e., minimum increase of the area and preservation of the quality of the drawing). We investigate computational complexity issues of variations of that problem, and we present polynomial time algorithms that find the minimum increase of space in one direction, needed to resolve overlaps, while preserving the orthogonal representation of the orthogonal drawing when objects have a predefined partial order.Algorithms2016-03-2892Article10.3390/a9020022221999-48932016-03-28doi: 10.3390/a9020022Konstantinos KakoulisIoannis Tollis<![CDATA[Algorithms, Vol. 9, Pages 21: Multivariate Algorithmics for Finding Cohesive Subnetworks]]>
http://www.mdpi.com/1999-4893/9/1/21
Community detection is an important task in the analysis of biological, social or technical networks. We survey different models of cohesive graphs, commonly referred to as clique relaxations, that are used in the detection of network communities. For each clique relaxation, we give an overview of basic model properties and of the complexity of the problem of finding large cohesive subgraphs under this model. Since this problem is usually NP-hard, we focus on combinatorial fixed-parameter algorithms exploiting typical structural properties of input networks.Algorithms2016-03-1691Article10.3390/a9010021211999-48932016-03-16doi: 10.3390/a9010021Christian Komusiewicz<![CDATA[Algorithms, Vol. 9, Pages 20: The Iterative Solution to Discrete-Time H∞ Control Problems for Periodic Systems]]>
http://www.mdpi.com/1999-4893/9/1/20
This paper addresses the problem of solving discrete-time H ∞ control problems for periodic systems. The approach for solving such a type of equations is well known in the literature. However, the focus of our research is set on the numerical computation of the stabilizing solution. In particular, two effective methods for practical realization of the known iterative processes are described. Furthermore, a new iterative approach is investigated and applied. On the basis of numerical experiments, we compare the presented methods. A major conclusion is that the new iterative approach is faster than rest of the methods and it uses less RAM memory than other methods.Algorithms2016-03-1491Article10.3390/a9010020201999-48932016-03-14doi: 10.3390/a9010020Ivan IvanovBoryana Bogdanova<![CDATA[Algorithms, Vol. 9, Pages 19: Review of Recent Advances in the Application of the Wavelet Transform to Diagnose Cracked Rotors]]>
http://www.mdpi.com/1999-4893/9/1/19
Wavelet transform (WT) has been used in the diagnosis of cracked rotors since the 1990s. At present, WT is one of the most commonly used tools to treat signals in several fields. Understandably, this has been an area of extensive scientific research, which is why this paper aims to summarize briefly the major advances in the field since 2008. The present review considers advances in the use and application of WT, the selection of the parameters used, and the key achievements in using WT for crack diagnosis.Algorithms2016-03-1491Review10.3390/a9010019191999-48932016-03-14doi: 10.3390/a9010019María GómezCristina CastejónJuan García-Prada<![CDATA[Algorithms, Vol. 9, Pages 18: Constructing Frozen Jacobian Iterative Methods for Solving Systems of Nonlinear Equations, Associated with ODEs and PDEs Using the Homotopy Method]]>
http://www.mdpi.com/1999-4893/9/1/18
A homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded parameters in the iterative methods with the help of the homotopy method: the values of the parameters are determined in such a way that a better convergence rate is achieved. The proposed homotopy technique is general and has the ability to construct different families of iterative methods, for solving weakly nonlinear systems of equations. Further iterative methods are also proposed for solving general systems of nonlinear equations.Algorithms2016-03-1191Article10.3390/a9010018181999-48932016-03-11doi: 10.3390/a9010018Uswah QasimZulifqar AliFayyaz AhmadStefano Serra-CapizzanoMalik Zaka UllahMir Asma<![CDATA[Algorithms, Vol. 9, Pages 17: Co-Clustering under the Maximum Norm]]>
http://www.mdpi.com/1999-4893/9/1/17
Co-clustering, that is partitioning a numerical matrix into “homogeneous” submatrices, has many applications ranging from bioinformatics to election analysis. Many interesting variants of co-clustering are NP-hard. We focus on the basic variant of co-clustering where the homogeneity of a submatrix is defined in terms of minimizing the maximum distance between two entries. In this context, we spot several NP-hard, as well as a number of relevant polynomial-time solvable special cases, thus charting the border of tractability for this challenging data clustering problem. For instance, we provide polynomial-time solvability when having to partition the rows and columns into two subsets each (meaning that one obtains four submatrices). When partitioning rows and columns into three subsets each, however, we encounter NP-hardness, even for input matrices containing only values from {0, 1, 2}.Algorithms2016-02-2591Article10.3390/a9010017171999-48932016-02-25doi: 10.3390/a9010017Laurent BulteauVincent FroeseSepp HartungRolf Niedermeier<![CDATA[Algorithms, Vol. 9, Pages 16: Multiband and Lossless Compression of Hyperspectral Images]]>
http://www.mdpi.com/1999-4893/9/1/16
Hyperspectral images are widely used in several real-life applications. In this paper, we investigate on the compression of hyperspectral images by considering different aspects, including the optimization of the computational complexity in order to allow implementations on limited hardware (i.e., hyperspectral sensors, etc.). We present an approach that relies on a three-dimensional predictive structure. Our predictive structure, 3D-MBLP, uses one or more previous bands as references to exploit the redundancies among the third dimension. The achieved results are comparable, and often better, with respect to the other state-of-art lossless compression techniques for hyperspectral images.Algorithms2016-02-1891Article10.3390/a9010016161999-48932016-02-18doi: 10.3390/a9010016Raffaele PizzolanteBruno Carpentieri<![CDATA[Algorithms, Vol. 9, Pages 15: A Geometric Orthogonal Projection Strategy for Computing the Minimum Distance Between a Point and a Spatial Parametric Curve]]>
http://www.mdpi.com/1999-4893/9/1/15
A new orthogonal projection method for computing the minimum distance between a point and a spatial parametric curve is presented. It consists of a geometric iteration which converges faster than the existing Newton’s method, and it is insensitive to the choice of initial values. We prove that projecting a point onto a spatial parametric curve under the method is globally second-order convergence.Algorithms2016-02-0691Article10.3390/a9010015151999-48932016-02-06doi: 10.3390/a9010015Xiaowu LiZhinan WuLinke HouLin WangChunguang YueQiao Xin<![CDATA[Algorithms, Vol. 9, Pages 14: Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems]]>
http://www.mdpi.com/1999-4893/9/1/14
In this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divided difference operator. The computational efficiency is compared with the existing methods. Numerical experiments support the theoretical results. Experimental results show that the new methods remarkably reduce the computing time in the process of high-precision computing.Algorithms2016-02-0191Article10.3390/a9010014141999-48932016-02-01doi: 10.3390/a9010014Xiaofeng WangXiaodong Fan<![CDATA[Algorithms, Vol. 9, Pages 13: Algorithms for Managing, Querying and Processing Big Data in Cloud Environments]]>
http://www.mdpi.com/1999-4893/9/1/13
Big data (e.g., [1–3]) has become one of the most challenging research topics in current years. Big data is everywhere, from social networks to web advertisements, from sensor and stream systems to bio-informatics, from graph management tools to smart cities, and so forth. [...]Algorithms2016-02-0191Editorial10.3390/a9010013131999-48932016-02-01doi: 10.3390/a9010013Alfredo Cuzzocrea<![CDATA[Algorithms, Vol. 9, Pages 12: Integrating Pareto Optimization into Dynamic Programming]]>
http://www.mdpi.com/1999-4893/9/1/12
Pareto optimization combines independent objectives by computing the Pareto front of the search space, yielding a set of optima where none scores better on all objectives than any other. Recently, it was shown that Pareto optimization seamlessly integrates with algebraic dynamic programming: when scoring schemes A and B can correctly evaluate the search space via dynamic programming, then so can Pareto optimization with respect to A and B. However, the integration of Pareto optimization into dynamic programming opens a wide range of algorithmic alternatives, which we study in substantial detail in this article, using real-world applications in biosequence analysis, a field where dynamic programming is ubiquitous. Our results are two-fold: (1) We introduce the operation of a “Pareto algebra product” in the dynamic programming framework of Bellman’s GAP. Users of this framework can now ask for Pareto optimization with a single keystroke. Careful evaluation of the implementation alternatives by means of an extended Bellman’s GAP compiler demonstrates the dependence of the best implementation choice on the application at hand. (2) We extract from our experiments several pieces of advice to programmers who do not use a system such as Bellman’s GAP, but who choose to hand-craft their dynamic programming recurrences, incorporating Pareto optimization from scratch.Algorithms2016-01-2791Article10.3390/a9010012121999-48932016-01-27doi: 10.3390/a9010012Thomas GatterRobert GiegerichCédric Saule<![CDATA[Algorithms, Vol. 9, Pages 11: Acknowledgement to Reviewers of Algorithms in 2015]]>
http://www.mdpi.com/1999-4893/9/1/11
The editors of Algorithms would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2015. [...]Algorithms2016-01-2291Editorial10.3390/a9010011111999-48932016-01-22doi: 10.3390/a9010011 Algorithms Editorial Office<![CDATA[Algorithms, Vol. 9, Pages 10: An Optimal Order Method for Multiple Roots in Case of Unknown Multiplicity]]>
http://www.mdpi.com/1999-4893/9/1/10
In the literature, recently, some three-step schemes involving four function evaluations for the solution of multiple roots of nonlinear equations, whose multiplicity is not known in advance, are considered, but they do not agree with Kung–Traub’s conjecture. The present article is devoted to the study of an iterative scheme for approximating multiple roots with a convergence rate of eight, when the multiplicity is hidden, which agrees with Kung–Traub’s conjecture. The theoretical study of the convergence rate is investigated and demonstrated. A few nonlinear problems are presented to justify the theoretical study.Algorithms2016-01-2291Article10.3390/a9010010101999-48932016-01-22doi: 10.3390/a9010010Jai Jaiswal<![CDATA[Algorithms, Vol. 9, Pages 9: NBTI-Aware Transient Fault Rate Analysis Method for Logic Circuit Based on Probability Voltage Transfer Characteristics]]>
http://www.mdpi.com/1999-4893/9/1/9
The reliability of Very Large Scale Integration (VLSI) circuits has become increasingly susceptible to transient faults induced by environmental noise with the scaling of technology. Some commonly used fault tolerance strategies require statistical methods to accurately estimate the fault rate in different parts of the logic circuit, and Monte Carlo (MC) simulation is often applied to complete this task. However, the MC method suffers from impractical computation costs due to the size of the circuits. Furthermore, circuit aging effects, such as negative bias temperature instability (NBTI), will change the characteristics of the circuit during its lifetime, leading to a change in the circuit’s noise margin. This change will increase the complexity of transient fault rate estimation tasks. In this paper, an NBTI-aware statistical analysis method based on probability voltage transfer characteristics is proposed for combinational logic circuit. This method can acquire accurate fault rates using a discrete probability density function approximation process, thus resolving the computation cost problem of the MC method. The proposed method can also consider aging effects and analyze statistical changes in the fault rates. Experimental results demonstrate that, compared to the MC simulation, our method can achieve computation times that are two orders of magnitude shorter while maintaining an error rate less than 9%.Algorithms2016-01-1891Article10.3390/a901000991999-48932016-01-18doi: 10.3390/a9010009Zhiming YangJunbao LiYang YuXiyuan Peng<![CDATA[Algorithms, Vol. 9, Pages 8: A Greedy Algorithm for Neighborhood Overlap-Based Community Detection]]>
http://www.mdpi.com/1999-4893/9/1/8
The neighborhood overlap (NOVER) of an edge u-v is defined as the ratio of the number of nodes who are neighbors for both u and v to that of the number of nodes who are neighbors of at least u or v. In this paper, we hypothesize that an edge u-v with a lower NOVER score bridges two or more sets of vertices, with very few edges (other than u-v) connecting vertices from one set to another set. Accordingly, we propose a greedy algorithm of iteratively removing the edges of a network in the increasing order of their neighborhood overlap and calculating the modularity score of the resulting network component(s) after the removal of each edge. The network component(s) that have the largest cumulative modularity score are identified as the different communities of the network. We evaluate the performance of the proposed NOVER-based community detection algorithm on nine real-world network graphs and compare the performance against the multi-level aggregation-based Louvain algorithm, as well as the original and time-efficient versions of the edge betweenness-based Girvan-Newman (GN) community detection algorithm.Algorithms2016-01-1191Article10.3390/a901000881999-48932016-01-11doi: 10.3390/a9010008Natarajan Meghanathan<![CDATA[Algorithms, Vol. 9, Pages 7: An Effective and Efficient MapReduce Algorithm for Computing BFS-Based Traversals of Large-Scale RDF Graphs]]>
http://www.mdpi.com/1999-4893/9/1/7
Nowadays, a leading instance of big data is represented by Web data that lead to the definition of so-called big Web data. Indeed, extending beyond to a large number of critical applications (e.g., Web advertisement), these data expose several characteristics that clearly adhere to the well-known 3V properties (i.e., volume, velocity, variety). Resource Description Framework (RDF) is a significant formalism and language for the so-called Semantic Web, due to the fact that a very wide family of Web entities can be naturally modeled in a graph-shaped manner. In this context, RDF graphs play a first-class role, because they are widely used in the context of modern Web applications and systems, including the emerging context of social networks. When RDF graphs are defined on top of big (Web) data, they lead to the so-called large-scale RDF graphs, which reasonably populate the next-generation Semantic Web. In order to process such kind of big data, MapReduce, an open source computational framework specifically tailored to big data processing, has emerged during the last years as the reference implementation for this critical setting. In line with this trend, in this paper, we present an approach for efficiently implementing traversals of large-scale RDF graphs over MapReduce that is based on the Breadth First Search (BFS) strategy for visiting (RDF) graphs to be decomposed and processed according to the MapReduce framework. We demonstrate how such implementation speeds-up the analysis of RDF graphs with respect to competitor approaches. Experimental results clearly support our contributions.Algorithms2016-01-1191Article10.3390/a901000771999-48932016-01-11doi: 10.3390/a9010007Alfredo CuzzocreaMirel CosulschiRoberto de Virgilio<![CDATA[Algorithms, Vol. 9, Pages 6: Efficient Metaheuristics for the Mixed Team Orienteering Problem with Time Windows]]>
http://www.mdpi.com/1999-4893/9/1/6
Given a graph whose nodes and edges are associated with a profit, a visiting (or traversing) time and an admittance time window, the Mixed Team Orienteering Problem with Time Windows (MTOPTW) seeks for a specific number of walks spanning a subset of nodes and edges of the graph so as to maximize the overall collected profit. The visit of the included nodes and edges should take place within their respective time window and the overall duration of each walk should be below a certain threshold. In this paper we introduce the MTOPTW, which can be used for modeling a realistic variant of the Tourist Trip Design Problem where the objective is the derivation of near-optimal multiple-day itineraries for tourists visiting a destination which features several points of interest (POIs) and scenic routes. Since the MTOPTW is a NP-hard problem, we propose the first metaheuristic approaches to tackle it. The effectiveness of our algorithms is validated through a number of experiments on POI and scenic route sets compiled from the city of Athens (Greece).Algorithms2016-01-0591Article10.3390/a901000661999-48932016-01-05doi: 10.3390/a9010006Damianos GavalasCharalampos KonstantopoulosKonstantinos MastakasGrammati PantziouNikolaos Vathis<![CDATA[Algorithms, Vol. 9, Pages 5: A Family of Iterative Methods for Solving Systems of Nonlinear Equations Having Unknown Multiplicity]]>
http://www.mdpi.com/1999-4893/9/1/5
The singularity of Jacobian happens when we are looking for a root, with multiplicity greater than one, of a system of nonlinear equations. The purpose of this article is two-fold. Firstly, we will present a modification of an existing method that computes roots with known multiplicities. Secondly, will propose the generalization of a family of methods for solving nonlinear equations with unknown multiplicities, to the system of nonlinear equations. The inclusion of a nonzero multi-variable auxiliary function is the key idea. Different choices of the auxiliary function give different families of the iterative method to find roots with unknown multiplicities. Few illustrative numerical experiments and a critical discussion end the paper.Algorithms2015-12-3191Article10.3390/a901000551999-48932015-12-31doi: 10.3390/a9010005Fayyaz AhmadS. Serra-CapizzanoMalik UllahA. Al-Fhaid<![CDATA[Algorithms, Vol. 9, Pages 4: A Novel Complex-Valued Encoding Grey Wolf Optimization Algorithm]]>
http://www.mdpi.com/1999-4893/9/1/4
Grey wolf optimization (GWO) is one of the recently proposed heuristic algorithms imitating the leadership hierarchy and hunting mechanism of grey wolves in nature. The aim of these algorithms is to perform global optimization. This paper presents a modified GWO algorithm based on complex-valued encoding; namely the complex-valued encoding grey wolf optimization (CGWO). We use CGWO to test 16 unconstrained benchmark functions with seven different scales and infinite impulse response (IIR) model identification. Compared to the real-valued GWO algorithm and other optimization algorithms; the CGWO performs significantly better in terms of accuracy; robustness; and convergence speed.Algorithms2015-12-3091Article10.3390/a901000441999-48932015-12-30doi: 10.3390/a9010004Qifang LuoSen ZhangZhiming LiYongquan Zhou<![CDATA[Algorithms, Vol. 9, Pages 3: Function Optimization and Parameter Performance Analysis Based on Gravitation Search Algorithm]]>
http://www.mdpi.com/1999-4893/9/1/3
The gravitational search algorithm (GSA) is a kind of swarm intelligence optimization algorithm based on the law of gravitation. The parameter initialization of all swarm intelligence optimization algorithms has an important influence on the global optimization ability. Seen from the basic principle of GSA, the convergence rate of GSA is determined by the gravitational constant and the acceleration of the particles. The optimization performances on six typical test functions are verified by the simulation experiments. The simulation results show that the convergence speed of the GSA algorithm is relatively sensitive to the setting of the algorithm parameters, and the GSA parameter can be used flexibly to improve the algorithm’s convergence velocity and improve the accuracy of the solutions.Algorithms2015-12-2491Article10.3390/a901000331999-48932015-12-24doi: 10.3390/a9010003Jie-Sheng WangJiang-Di Song<![CDATA[Algorithms, Vol. 9, Pages 1: On the Kung-Traub Conjecture for Iterative Methods for Solving Quadratic Equations]]>
http://www.mdpi.com/1999-4893/9/1/1
Kung-Traub’s conjecture states that an optimal iterative method based on d function evaluations for finding a simple zero of a nonlinear function could achieve a maximum convergence order of 2 d−1. During the last years, many attempts have been made to prove this conjecture or develop optimal methods which satisfy the conjecture. We understand from the conjecture that the maximum order reached by a method with three function evaluations is four, even for quadratic functions. In this paper, we show that the conjecture fails for quadratic functions. In fact, we can find a 2-point method with three function evaluations reaching fifth order convergence. We also develop 2-point 3rd to 8th order methods with one function and two first derivative evaluations using weight functions. Furthermore, we show that with the same number of function evaluations we can develop higher order 2-point methods of order r + 2 , where r is a positive integer, ≥ 1 . We also show that we can develop a higher order method with the same number of function evaluations if we know the asymptotic error constant of the previous method. We prove the local convergence of these methods which we term as Babajee’s Quadratic Iterative Methods and we extend these methods to systems involving quadratic equations. We test our methods with some numerical experiments including an application to Chandrasekhar’s integral equation arising in radiative heat transfer theory.Algorithms2015-12-2491Article10.3390/a901000111999-48932015-12-24doi: 10.3390/a9010001Diyashvir Babajee<![CDATA[Algorithms, Vol. 9, Pages 2: Offset-Assisted Factored Solution of Nonlinear Systems]]>
http://www.mdpi.com/1999-4893/9/1/2
This paper presents an improvement to the recently-introduced factored method for the solution of nonlinear equations. The basic idea consists of transforming the original system by adding an offset to all unknowns. When searching for real solutions, a real offset prevents the intermediate values of unknowns from becoming complex. Reciprocally, when searching for complex solutions, a complex offset is advisable to allow the iterative process to quickly abandon the real domain. Several examples are used to illustrate the performance of the proposed algorithm, when compared to Newton’s method.Algorithms2015-12-2391Article10.3390/a901000221999-48932015-12-23doi: 10.3390/a9010002José Ruiz-OltraCatalina Gómez-QuilesAntonio Gómez-Expósito<![CDATA[Algorithms, Vol. 8, Pages 1210-1218: Numerical Properties of Different Root-Finding Algorithms Obtained for Approximating Continuous Newton’s Method]]>
http://www.mdpi.com/1999-4893/8/4/1210
This paper is dedicated to the study of continuous Newton’s method, which is a generic differential equation whose associated flow tends to the zeros of a given polynomial. Firstly, we analyze some numerical features related to the root-finding methods obtained after applying different numerical methods for solving initial value problems. The relationship between the step size and the order of convergence is particularly considered. We have analyzed both the cases of a constant and non-constant step size in the procedure of integration. We show that working with a non-constant step, the well-known Chebyshev-Halley family of iterative methods for solving nonlinear scalar equations is obtained.Algorithms2015-12-1784Article10.3390/a8041210121012181999-48932015-12-17doi: 10.3390/a8041210José Gutiérrez<![CDATA[Algorithms, Vol. 8, Pages 1195-1209: A New Smoothing Conjugate Gradient Method for Solving Nonlinear Nonsmooth Complementarity Problems]]>
http://www.mdpi.com/1999-4893/8/4/1195
In this paper, by using the smoothing Fischer-Burmeister function, we present a new smoothing conjugate gradient method for solving the nonlinear nonsmooth complementarity problems. The line search which we used guarantees the descent of the method. Under suitable conditions, the new smoothing conjugate gradient method is proved globally convergent. Finally, preliminary numerical experiments show that the new method is efficient.Algorithms2015-12-1784Article10.3390/a8041195119512091999-48932015-12-17doi: 10.3390/a8041195Ajie ChuShouqiang DuYixiao Su<![CDATA[Algorithms, Vol. 8, Pages 1175-1194: A Data Analytic Algorithm for Managing, Querying, and Processing Uncertain Big Data in Cloud Environments]]>
http://www.mdpi.com/1999-4893/8/4/1175
Big data are everywhere as high volumes of varieties of valuable precise and uncertain data can be easily collected or generated at high velocity in various real-life applications. Embedded in these big data are rich sets of useful information and knowledge. To mine these big data and to discover useful information and knowledge, we present a data analytic algorithm in this article. Our algorithm manages, queries, and processes uncertain big data in cloud environments. More specifically, it manages transactions of uncertain big data, allows users to query these big data by specifying constraints expressing their interests, and processes the user-specified constraints to discover useful information and knowledge from the uncertain big data. As each item in every transaction in these uncertain big data is associated with an existential probability value expressing the likelihood of that item to be present in a particular transaction, computation could be intensive. Our algorithm uses the MapReduce model on a cloud environment for effective data analytics on these uncertain big data. Experimental results show the effectiveness of our data analytic algorithm for managing, querying, and processing uncertain big data in cloud environments.Algorithms2015-12-1184Article10.3390/a8041175117511941999-48932015-12-11doi: 10.3390/a8041175Fan JiangCarson Leung<![CDATA[Algorithms, Vol. 8, Pages 1143-1174: Generating Realistic Labelled, Weighted Random Graphs]]>
http://www.mdpi.com/1999-4893/8/4/1143
Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs) with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI) approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs). Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.Algorithms2015-12-0884Article10.3390/a8041143114311741999-48932015-12-08doi: 10.3390/a8041143Michael DavisZhanyu MaWeiru LiuPaul MillerRuth HunterFrank Kee<![CDATA[Algorithms, Vol. 8, Pages 1129-1142: Efficiency Intra-Cluster Device-to-Device Relay Selection for Multicast Services Based on Combinatorial Auction]]>
http://www.mdpi.com/1999-4893/8/4/1129
In Long Term Evolution-Advanced (LTE-A) networks, Device-to-device (D2D) communications can be utilized to enhance the performance of multicast services by leveraging D2D relays to serve nodes with worse channel conditions within a cluster. For traditional D2D relay schemes, D2D links with poor channel condition may be the bottleneck of system sum data rate. In this paper, to optimize the throughput of D2D communications, we introduce an iterative combinatorial auction algorithm for efficient D2D relay selection. In combinatorial auctions, the User Equipments (UEs) that fails to correctly receive multicast data from eNodeB (eNB) are viewed as bidders that compete for D2D relays, while the eNB is treated as the auctioneer. We also give properties of convergency and low-complexity and present numerical simulations to verify the efficiency of the proposed algorithm.Algorithms2015-12-0284Article10.3390/a8041129112911421999-48932015-12-02doi: 10.3390/a8041129Yong ZhangFangmin Li<![CDATA[Algorithms, Vol. 8, Pages 1121-1128: On the Local Convergence of a Third Order Family of Iterative Processes]]>
http://www.mdpi.com/1999-4893/8/4/1121
Efficiency is generally the most important aspect to take into account when choosing an iterative method to approximate a solution of an equation, but is not the only aspect to consider in the iterative process. Another important aspect to consider is the accessibility of the iterative process, which shows the domain of starting points from which the iterative process converges to a solution of the equation. So, we consider a family of iterative processes with a higher efficiency index than Newton’s method. However, this family of proecsses presents problems of accessibility to the solution x * . From a local study of the convergence of this family, we perform an optimization study of the accessibility and obtain iterative processes with better accessibility than Newton’s method.Algorithms2015-12-0184Article10.3390/a8041121112111281999-48932015-12-01doi: 10.3390/a8041121M. Hernández-VerónN. Romero<![CDATA[Algorithms, Vol. 8, Pages 1111-1120: An Optimal Biparametric Multipoint Family and Its Self-Acceleration with Memory for Solving Nonlinear Equations]]>
http://www.mdpi.com/1999-4893/8/4/1111
In this paper, a family of Steffensen-type methods of optimal order of convergence with two parameters is constructed by direct Newtonian interpolation. It satisfies the conjecture proposed by Kung and Traub (J. Assoc. Comput. Math. 1974, 21, 634–651) that an iterative method based on m evaluations per iteration without memory would arrive at the optimal convergence of order 2m-1 . Furthermore, the family of Steffensen-type methods of super convergence is suggested by using arithmetic expressions for the parameters with memory but no additional new evaluation of the function. Their error equations, asymptotic convergence constants and convergence orders are obtained. Finally, they are compared with related root-finding methods in the numerical examples.Algorithms2015-12-0184Article10.3390/a8041111111111201999-48932015-12-01doi: 10.3390/a8041111Quan ZhengXin ZhaoYufeng Liu<![CDATA[Algorithms, Vol. 8, Pages 1088-1110: Computer Aided Diagnosis System for Early Lung Cancer Detection]]>
http://www.mdpi.com/1999-4893/8/4/1088
Lung cancer continues to rank as the leading cause of cancer deaths worldwide. One of the most promising techniques for early detection of cancerous cells relies on sputum cell analysis. This was the motivation behind the design and the development of a new computer aided diagnosis (CAD) system for early detection of lung cancer based on the analysis of sputum color images. The proposed CAD system encompasses four main processing steps. First is the preprocessing step which utilizes a Bayesian classification method using histogram analysis. Then, in the second step, mean shift segmentation is applied to segment the nuclei from the cytoplasm. The third step is the feature analysis. In this step, geometric and chromatic features are extracted from the nucleus region. These features are used in the diagnostic process of the sputum images. Finally, the diagnosis is completed using an artificial neural network and support vector machine (SVM) for classifying the cells into benign or malignant. The performance of the system was analyzed based on different criteria such as sensitivity, specificity and accuracy. The evaluation was carried out using Receiver Operating Characteristic (ROC) curve. The experimental results demonstrate the efficiency of the SVM classifier over other classifiers, with 97% sensitivity and accuracy as well as a significant reduction in the number of false positive and false negative rates.Algorithms2015-11-2084Article10.3390/a8041088108811101999-48932015-11-20doi: 10.3390/a8041088Fatma TaherNaoufel WerghiHussain Al-Ahmad<![CDATA[Algorithms, Vol. 8, Pages 1076-1087: Local Convergence of an Efﬁcient High Convergence Order Method Using Hypothesis Only on the First Derivative]]>
http://www.mdpi.com/1999-4893/8/4/1076
We present a local convergence analysis of an eighth order three step methodin order to approximate a locally unique solution of nonlinear equation in a Banach spacesetting. In an earlier study by Sharma and Arora (2015), the order of convergence wasshown using Taylor series expansions and hypotheses up to the fourth order derivative oreven higher of the function involved which restrict the applicability of the proposed scheme. However, only ﬁrst order derivative appears in the proposed scheme. In order to overcomethis problem, we proposed the hypotheses up to only the ﬁrst order derivative. In this way,we not only expand the applicability of the methods but also propose convergence domain. Finally, where earlier studies cannot be applied, a variety of concrete numerical examplesare proposed to obtain the solutions of nonlinear equations. Our study does not exhibit thistype of problem/restriction.Algorithms2015-11-2084Article10.3390/a8041076107610871999-48932015-11-20doi: 10.3390/a8041076Ioannis ArgyrosRamandeep BehlS.S. Motsa<![CDATA[Algorithms, Vol. 8, Pages 1052-1075: A New Approach for Automatic Removal of Movement Artifacts in Near-Infrared Spectroscopy Time Series by Means of Acceleration Data]]>
http://www.mdpi.com/1999-4893/8/4/1052
Near-infrared spectroscopy (NIRS) enables the non-invasive measurement of changes in hemodynamics and oxygenation in tissue. Changes in light-coupling due to movement of the subject can cause movement artifacts (MAs) in the recorded signals. Several methods have been developed so far that facilitate the detection and reduction of MAs in the data. However, due to fixed parameter values (e.g., global threshold) none of these methods are perfectly suitable for long-term (i.e., hours) recordings or were not time-effective when applied to large datasets. We aimed to overcome these limitations by automation, i.e., data adaptive thresholding specifically designed for long-term measurements, and by introducing a stable long-term signal reconstruction. Our new technique (“acceleration-based movement artifact reduction algorithm”, AMARA) is based on combining two methods: the “movement artifact reduction algorithm” (MARA, Scholkmann et al. Phys. Meas. 2010, 31, 649–662), and the “accelerometer-based motion artifact removal” (ABAMAR, Virtanen et al. J. Biomed. Opt. 2011, 16, 087005). We describe AMARA in detail and report about successful validation of the algorithm using empirical NIRS data, measured over the prefrontal cortex in adolescents during sleep. In addition, we compared the performance of AMARA to that of MARA and ABAMAR based on validation data.Algorithms2015-11-1984Article10.3390/a8041052105210751999-48932015-11-19doi: 10.3390/a8041052Andreas MetzMartin WolfPeter AchermannFelix Scholkmann<![CDATA[Algorithms, Vol. 8, Pages 1035-1051: Natalie 2.0: Sparse Global Network Alignment as a Special Case of Quadratic Assignment]]>
http://www.mdpi.com/1999-4893/8/4/1035
Data on molecular interactions is increasing at a tremendous pace, while the development of solid methods for analyzing this network data is still lagging behind. This holds in particular for the field of comparative network analysis, where one wants to identify commonalities between biological networks. Since biological functionality primarily operates at the network level, there is a clear need for topology-aware comparison methods. We present a method for global network alignment that is fast and robust and can flexibly deal with various scoring schemes taking both node-to-node correspondences as well as network topologies into account. We exploit that network alignment is a special case of the well-studied quadratic assignment problem (QAP). We focus on sparse network alignment, where each node can be mapped only to a typically small subset of nodes in the other network. This corresponds to a QAP instance with a symmetric and sparse weight matrix. We obtain strong upper and lower bounds for the problem by improving a Lagrangian relaxation approach and introduce the open source software tool Natalie 2.0, a publicly available implementation of our method. In an extensive computational study on protein interaction networks for six different species, we find that our new method outperforms alternative established and recent state-of-the-art methods.Algorithms2015-11-1884Article10.3390/a8041035103510511999-48932015-11-18doi: 10.3390/a8041035Mohammed El-KebirJaap HeringaGunnar Klau<![CDATA[Algorithms, Vol. 8, Pages 1021-1034: Semi-Supervised Classification Based on Mixture Graph]]>
http://www.mdpi.com/1999-4893/8/4/1021
Graph-based semi-supervised classification heavily depends on a well-structured graph. In this paper, we investigate a mixture graph and propose a method called semi-supervised classification based on mixture graph (SSCMG). SSCMG first constructs multiple k nearest neighborhood (kNN) graphs in different random subspaces of the samples. Then, it combines these graphs into a mixture graph and incorporates this graph into a graph-based semi-supervised classifier. SSCMG can preserve the local structure of samples in subspaces and is less affected by noisy and redundant features. Empirical study on facial images classification shows that SSCMG not only has better recognition performance, but also is more robust to input parameters than other related methods.Algorithms2015-11-1684Article10.3390/a8041021102110341999-48932015-11-16doi: 10.3390/a8041021Lei FengGuoxian Yu<![CDATA[Algorithms, Vol. 8, Pages 999-1020: An Integer Linear Programming Formulation for the Minimum Cardinality Segmentation Problem]]>
http://www.mdpi.com/1999-4893/8/4/999
In this article, we investigate the Minimum Cardinality Segmentation Problem (MCSP), an NP-hard combinatorial optimization problem arising in intensity-modulated radiation therapy. The problem consists in decomposing a given nonnegative integer matrix into a nonnegative integer linear combination of a minimum cardinality set of binary matrices satisfying the consecutive ones property. We show how to transform the MCSP into a combinatorial optimization problem on a weighted directed network and we exploit this result to develop an integer linear programming formulation to exactly solve it. Computational experiments show that the lower bounds obtained by the linear relaxation of the considered formulation improve upon those currently described in the literature and suggest, at the same time, new directions for the development of future exact solution approaches to the problem.Algorithms2015-11-1184Article10.3390/a804099999910201999-48932015-11-11doi: 10.3390/a8040999Daniele CatanzaroCéline Engelbeen<![CDATA[Algorithms, Vol. 8, Pages 982-998: Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations]]>
http://www.mdpi.com/1999-4893/8/4/982
An application of iterative methods for computing the Moore–Penrose inverse in balancing chemical equations is considered. With the aim to illustrate proposed algorithms, an improved high order hyper-power matrix iterative method for computing generalized inverses is introduced and applied. The improvements of the hyper-power iterative scheme are based on its proper factorization, as well as on the possibility to accelerate the iterations in the initial phase of the convergence. Although the effectiveness of our approach is confirmed on the basis of the theoretical point of view, some numerical comparisons in balancing chemical equations, as well as on randomly-generated matrices are furnished.Algorithms2015-11-0384Article10.3390/a80409829829981999-48932015-11-03doi: 10.3390/a8040982Farahnaz SoleimaniPredrag Stanimirovi´cFazlollah Soleymani<![CDATA[Algorithms, Vol. 8, Pages 965-981: A Particle Filter Track-Before-Detect Algorithm Based on Hybrid Differential Evolution]]>
http://www.mdpi.com/1999-4893/8/4/965
In this paper, we address the problem of detecting and tracking targets with a low signal-to-noise ratio (SNR) by exploiting hybrid differential evolution (HDE) in the particle filter track-before-detect (PF-TBD) context. Firstly, we introduce the Bayesian PF-TBD method and its weaknesses. Secondly, the HDE algorithm is regarded as a novel particle updating strategy, which is proposed to optimize the performance of the PF-TBD algorithm. Thirdly, we combine the systematic resampling approach to enhance the performance of the proposed algorithm. Then, an improved PF-TBD algorithm based on the HDE method is proposed. Experiment results indicate that the proposed method has better performance in detecting and tracking than previous algorithms when the targets have a low SNR.Algorithms2015-11-0384Article10.3390/a80409659659811999-48932015-11-03doi: 10.3390/a8040965Chaozhu ZhangLin LiYu Wang<![CDATA[Algorithms, Vol. 8, Pages 951-964: A New Swarm Intelligence Approach for Clustering Based on Krill Herd with Elitism Strategy]]>
http://www.mdpi.com/1999-4893/8/4/951
As one of the most popular and well-recognized clustering methods, fuzzy C-means (FCM) clustering algorithm is the basis of other fuzzy clustering analysis methods in theory and application respects. However, FCM algorithm is essentially a local search optimization algorithm. Therefore, sometimes, it may fail to find the global optimum. For the purpose of getting over the disadvantages of FCM algorithm, a new version of the krill herd (KH) algorithm with elitism strategy, called KHE, is proposed to solve the clustering problem. Elitism tragedy has a strong ability of preventing the krill population from degrading. In addition, the well-selected parameters are used in the KHE method instead of originating from nature. Through an array of simulation experiments, the results show that the KHE is indeed a good choice for solving general benchmark problems and fuzzy clustering analyses.Algorithms2015-10-2284Article10.3390/a80409519519641999-48932015-10-22doi: 10.3390/a8040951Zhi-Yong LiJiao-Hong YiGai-Ge Wang<![CDATA[Algorithms, Vol. 8, Pages 929-950: Series Arc Fault Detection Algorithm Based on Autoregressive Bispectrum Analysis]]>
http://www.mdpi.com/1999-4893/8/4/929
Arc fault is one of the most critical reasons for electrical fires. Due to the diversity, randomness and concealment of arc faults in low-voltage circuits, it is difficult for general methods to protect all loads from series arc faults. From the analysis of many series arc faults, a large number of high frequency signals generated in circuits are found. These signals are easily affected by Gaussian noise which is difficult to be eliminated as a result of frequency aliasing. Thus, a novel detection algorithm is developed to accurately detect series arc faults in this paper. Initially, an autoregressive model of the mixed high frequency signals is modelled. Then, autoregressive bispectrum analysis is introduced to analyze common series arc fault features. The phase information of arc fault signal is preserved using this method. The influence of Gaussian noise is restrained effectively. Afterwards, several features including characteristic frequency, fluctuation of phase angles, diffused distribution and incremental numbers of bispectrum peaks are extracted for recognizing arc faults. Finally, least squares support vector machine is used to accurately identify series arc faults from the load states based on these frequency features of bispectrum. The validity of the algorithm is experimentally verified obtaining arc fault detection rate above 97%.Algorithms2015-10-1684Article10.3390/a80409299299501999-48932015-10-16doi: 10.3390/a8040929Kai YangRencheng ZhangShouhong ChenFujiang ZhangJianhong YangXingbin Zhang<![CDATA[Algorithms, Vol. 8, Pages 910-928: Effective Data Acquisition Protocol for Multi-Hop Heterogeneous Wireless Sensor Networks Using Compressive Sensing]]>
http://www.mdpi.com/1999-4893/8/4/910
In designing wireless sensor networks (WSNs), it is important to reduce energy dissipation and prolong network lifetime. Clustering of nodes is one of the most effective approaches for conserving energy in WSNs. Cluster formation protocols generally consider the heterogeneity of sensor nodes in terms of energy difference of nodes but ignore the different transmission ranges of them. In this paper, we propose an effective data acquisition clustered protocol using compressive sensing (EDACP-CS) for heterogeneous WSNs that aims to conserve the energy of sensor nodes in the presence of energy and transmission range heterogeneity. In EDACP-CS, cluster heads are selected based on the distance from the base station and sensor residual energy. Simulation results show that our protocol offers a much better performance than the existing protocols in terms of energy consumption, stability, network lifetime, and throughput.Algorithms2015-10-1684Article10.3390/a80409109109281999-48932015-10-16doi: 10.3390/a8040910Ahmed Khedr<![CDATA[Algorithms, Vol. 8, Pages 895-909: On Some Improved Harmonic Mean Newton-Like Methods for Solving Systems of Nonlinear Equations]]>
http://www.mdpi.com/1999-4893/8/4/895
In this work, we have developed a fourth order Newton-like method based on harmonic mean and its multi-step version for solving system of nonlinear equations. The new fourth order method requires evaluation of one function and two first order Fréchet derivatives for each iteration. The multi-step version requires one more function evaluation for each iteration. The proposed new scheme does not require the evaluation of second or higher order Fréchet derivatives and still reaches fourth order convergence. The multi-step version converges with order 2r+4, where r is a positive integer and r ≥ 1. We have proved that the root α is a point of attraction for a general iterative function, whereas the proposed new schemes also satisfy this result. Numerical experiments including an application to 1-D Bratu problem are given to illustrate the efficiency of the new methods. Also, the new methods are compared with some existing methods.Algorithms2015-10-0984Article10.3390/a80408958959091999-48932015-10-09doi: 10.3390/a8040895Diyashvir BabajeeKalyanasundaram MadhuJayakumar Jayaraman<![CDATA[Algorithms, Vol. 8, Pages 870-894: Code Synchronization Algorithm Based on Segment Correlation in Spread Spectrum Communication]]>
http://www.mdpi.com/1999-4893/8/4/870
Spread Spectrum (SPSP) Communication is the theoretical basis of Direct Sequence Spread Spectrum (DSSS) transceiver technology. Spreading code, modulation, demodulation, carrier synchronization and code synchronization in SPSP communications are the core parts of DSSS transceivers. This paper focuses on the code synchronization problem in SPSP communications. A novel code synchronization algorithm based on segment correlation is proposed. The proposed algorithm can effectively deal with the informational misjudgment caused by the unreasonable data acquisition times. This misjudgment may lead to an inability of DSSS receivers to restore transmitted signals. Simulation results show the feasibility of a DSSS transceiver design based on the proposed code synchronization algorithm. Finally, the communication functions of the DSSS transceiver based on the proposed code synchronization algorithm are implemented on Field Programmable Gate Array (FPGA).Algorithms2015-10-0984Article10.3390/a80408708708941999-48932015-10-09doi: 10.3390/a8040870Aohan LiZiheng YangRenji QiFeng ZhouGuangjie Han<![CDATA[Algorithms, Vol. 8, Pages 850-869: Automatic Classification of Protein Structure Using the Maximum Contact Map Overlap Metric]]>
http://www.mdpi.com/1999-4893/8/4/850
In this work, we propose a new distance measure for comparing two protein structures based on their contact map representations. We show that our novel measure, which we refer to as the maximum contact map overlap (max-CMO) metric, satisfies all properties of a metric on the space of protein representations. Having a metric in that space allows one to avoid pairwise comparisons on the entire database and, thus, to significantly accelerate exploring the protein space compared to no-metric spaces. We show on a gold standard superfamily classification benchmark set of 6759 proteins that our exact k-nearest neighbor (k-NN) scheme classifies up to 224 out of 236 queries correctly and on a larger, extended version of the benchmark with 60; 850 additional structures, up to 1361 out of 1369 queries. Our k-NN classification thus provides a promising approach for the automatic classification of protein structures based on flexible contact map overlap alignments.Algorithms2015-10-0984Article10.3390/a80408508508691999-48932015-10-09doi: 10.3390/a8040850Rumen AndonovHristo DjidjevGunnar KlauMathilde Boudic-JaminInken Wohlers<![CDATA[Algorithms, Vol. 8, Pages 832-849: Newton-Type Methods on Generalized Banach Spaces and Applications in Fractional Calculus]]>
http://www.mdpi.com/1999-4893/8/4/832
We present a semilocal convergence study of Newton-type methods on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies require that the operator involved is Fréchet differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of Newton-type methods to include fractional calculus and problems from other areas. Moreover, under the same or weaker conditions, we obtain weaker sufficient convergence criteria, tighter error bounds on the distances involved and an at least as precise information on the location of the solution. Special cases are provided where the old convergence criteria cannot apply but the new criteria can apply to locate zeros of operators. Some applications include fractional calculus involving the Riemann-Liouville fractional integral and the Caputo fractional derivative. Fractional calculus is very important for its applications in many applied sciences.Algorithms2015-10-0984Article10.3390/a80408328328491999-48932015-10-09doi: 10.3390/a8040832George AnastassiouIoannis Argyros<![CDATA[Algorithms, Vol. 8, Pages 810-831: Finding Supported Paths in Heterogeneous Networks]]>
http://www.mdpi.com/1999-4893/8/4/810
Subnetwork mining is an essential issue in the analysis of biological, social and communication networks. Recent applications require the simultaneous mining of several networks on the same or a similar vertex set. That is, one searches for subnetworks fulfilling different properties in each input network. We study the case that the input consists of a directed graph D and an undirected graph G on the same vertex set, and the sought pattern is a path P in D whose vertex set induces a connected subgraph of G. In this context, three concrete problems arise, depending on whether the existence of P is questioned or whether the length of P is to be optimized: in that case, one can search for a longest path or (maybe less intuitively) a shortest one. These problems have immediate applications in biological networks and predictable applications in social, information and communication networks. We study the classic and parameterized complexity of the problem, thus identifying polynomial and NP-complete cases, as well as fixed-parameter tractable and W[1]-hard cases. We also propose two enumeration algorithms that we evaluate on synthetic and biological data.Algorithms2015-10-0984Article10.3390/a80408108108311999-48932015-10-09doi: 10.3390/a8040810Guillaume FertinChristian KomusiewiczHafedh Mohamed-BabouIrena Rusu<![CDATA[Algorithms, Vol. 8, Pages 799-809: Reweighted Factor Selection for SLMS-RL1 Algorithm under Gaussian Mixture Noise Environments]]>
http://www.mdpi.com/1999-4893/8/4/799
The sign least mean square with reweighted L1-norm constraint (SLMS-RL1) algorithm is an attractive sparse channel estimation method among Gaussian mixture model (GMM) based algorithms for use in impulsive noise environments. The channel sparsity can be exploited by SLMS-RL1 algorithm based on appropriate reweighted factor, which is one of key parameters to adjust the sparse constraint for SLMS-RL1 algorithm. However, to the best of the authors’ knowledge, a reweighted factor selection scheme has not been developed. This paper proposes a Monte-Carlo (MC) based reweighted factor selection method to further strengthen the performance of SLMS-RL1 algorithm. To validate the performance of SLMS-RL1 using the proposed reweighted factor, simulations results are provided to demonstrate that convergence speed can be reduced by increasing the channel sparsity, while the steady-state MSE performance only slightly changes with different GMM impulsive-noise strengths.Algorithms2015-09-2584Article10.3390/a80407997998091999-48932015-09-25doi: 10.3390/a8040799Tingping ZhangGuan Gui<![CDATA[Algorithms, Vol. 8, Pages 786-798: A Family of Newton Type Iterative Methods for Solving Nonlinear Equations]]>
http://www.mdpi.com/1999-4893/8/3/786
In this paper, a general family of n-point Newton type iterative methods for solving nonlinear equations is constructed by using direct Hermite interpolation. The order of convergence of the new n-point iterative methods without memory is 2n requiring the evaluations of n functions and one first-order derivative in per full iteration, which implies that this family is optimal according to Kung and Traub’s conjecture (1974). Its error equations and asymptotic convergence constants are obtained. The n-point iterative methods with memory are obtained by using a self-accelerating parameter, which achieve much faster convergence than the corresponding n-point methods without memory. The increase of convergence order is attained without any additional calculations so that the n-point Newton type iterative methods with memory possess a very high computational efficiency. Numerical examples are demonstrated to confirm theoretical results.Algorithms2015-09-2283Article10.3390/a80307867867981999-48932015-09-22doi: 10.3390/a8030786Xiaofeng WangYuping QinWeiyi QianSheng ZhangXiaodong Fan<![CDATA[Algorithms, Vol. 8, Pages 774-785: Parallel Variants of Broyden’s Method]]>
http://www.mdpi.com/1999-4893/8/3/774
In this paper we investigate some parallel variants of Broyden’s method and, for the basic variant, we present its convergence properties. The main result is that the behavior of the considered parallel Broyden’s variants is comparable with the classical parallel Newton method, and significantly better than the parallel Cimmino method, both for linear and nonlinear cases. The considered variants are also compared with two more recently proposed parallel Broyden’s method. Some numerical experiments are presented to illustrate the advantages and limits of the proposed algorithms.Algorithms2015-09-1583Article10.3390/a80307747747851999-48932015-09-15doi: 10.3390/a8030774Ioan BistranStefan MarusterLiviu Mafteiu-Scai<![CDATA[Algorithms, Vol. 8, Pages 754-773: Modified Classical Graph Algorithms for the DNA Fragment Assembly Problem]]>
http://www.mdpi.com/1999-4893/8/3/754
DNA fragment assembly represents an important challenge to the development of efficient and practical algorithms due to the large number of elements to be assembled. In this study, we present some graph theoretical linear time algorithms to solve the problem. To achieve linear time complexity, a heap with constant time operations was developed, for the special case where the edge weights are integers and do not depend on the problem size. The experiments presented show that modified classical graph theoretical algorithms can solve the DNA fragment assembly problem efficiently.Algorithms2015-09-1083Article10.3390/a80307547547731999-48932015-09-10doi: 10.3390/a8030754Guillermo Mallén-FullertonJ. Quiroz-IbarraAntonio MirandaGuillermo Fernández-Anaya<![CDATA[Algorithms, Vol. 8, Pages 743-753: A CS Recovery Algorithm for Model and Time Delay Identification of MISO-FIR Systems]]>
http://www.mdpi.com/1999-4893/8/3/743
This paper considers identifying the multiple input single output finite impulse response (MISO-FIR) systems with unknown time delays and orders. Generally, parameters, orders and time delays of an MISO system are separately identified from different algorithms. In this paper, we aim to perform the model identification and time delay estimation simultaneously from a limited number of observations. For an MISO-FIR system with many inputs and unknown input time delays, the corresponding identification model contains a large number of parameters, requiring a great number of observations for identification and leading to a heavy computational burden. Inspired by the compressed sensing (CS) recovery theory, a threshold orthogonal matching pursuit algorithm (TH-OMP) is presented to simultaneously identify the parameters, the orders and the time delays of the MISO-FIR systems. The proposed algorithm requires only a small number of sampled data compared to the conventional identification methods, such as the least squares method. The effectiveness of the proposed algorithm is verified by simulation results.Algorithms2015-09-1083Article10.3390/a80307437437531999-48932015-09-10doi: 10.3390/a8030743Yanjun LiuTaiyang Tao<![CDATA[Algorithms, Vol. 8, Pages 723-742: A Comparative Study of Modern Heuristics on the School Timetabling Problem]]>
http://www.mdpi.com/1999-4893/8/3/723
In this contribution a comparative study of modern heuristics on the school timetabling problem is presented. More precisely, we investigate the application of two population-based algorithms, namely a Particle Swarm Optimization (PSO) and an Artificial Fish Swarm (AFS), on the high school timetabling problem. In order to demonstrate their efficiency and performance, experiments with real-world input data have been performed. Both algorithms proposed manage to create feasible and efficient high school timetables, thus fulfilling adequately the timetabling needs of the respective high schools. Computational results demonstrate that both algorithms manage to reach efficient solutions, most of the times better than existing approaches applied to the same school timetabling input instances using the same evaluation criteria.Algorithms2015-08-2883Article10.3390/a80307237237421999-48932015-08-28doi: 10.3390/a8030723Iosif KatsaragakisIoannis TassopoulosGrigorios Beligiannis<![CDATA[Algorithms, Vol. 8, Pages 712-722: Gradient-Based Iterative Identification for Wiener Nonlinear Dynamic Systems with Moving Average Noises]]>
http://www.mdpi.com/1999-4893/8/3/712
This paper focuses on the parameter identification problem for Wiener nonlinear dynamic systems with moving average noises. In order to improve the convergence rate, the gradient-based iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates, and to compute iteratively the noise estimates based on the obtained parameter estimates. The simulation results show that the proposed algorithm can effectively estimate the parameters of Wiener systems with moving average noises.Algorithms2015-08-2683Article10.3390/a80307127127221999-48932015-08-26doi: 10.3390/a8030712Lincheng ZhouXiangli LiHuigang XuPeiyi Zhu<![CDATA[Algorithms, Vol. 8, Pages 697-711: Comparative Study of DE, PSO and GA for Position Domain PID Controller Tuning]]>
http://www.mdpi.com/1999-4893/8/3/697
Gain tuning is very important in order to obtain good performances for a given controller. Contour tracking performance is mainly determined by the selected control gains of a position domain PID controller. In this paper, three popular evolutionary algorithms are utilized to optimize the gains of a position domain PID controller for performance improvement of contour tracking of robotic manipulators. Differential Evolution (DE), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) are used to determine the optimal gains of the position domain PID controller, and three distinct fitness functions are also used to quantify the contour tracking performance of each solution set. Simulation results show that DE features the highest performance indexes for both linear and nonlinear contour tracking, while PSO is quite efficient for linear contour tracking. Both algorithms performed consistently better than GA that featured premature convergence in all cases.Algorithms2015-08-2183Article10.3390/a80306976977111999-48932015-08-21doi: 10.3390/a8030697Puren OuyangVangjel Pano<![CDATA[Algorithms, Vol. 8, Pages 680-696: Network Community Detection on Metric Space]]>
http://www.mdpi.com/1999-4893/8/3/680
Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the objective function, and then, one uses various heuristics to solve the optimization problem to extract the interesting communities for the user. In this article, we demonstrate the procedure to transform a graph into points of a metric space and develop the methods of community detection with the help of a metric defined for a pair of points. We have also studied and analyzed the community structure of the network therein. The results obtained with our approach are very competitive with most of the well-known algorithms in the literature, and this is justified over the large collection of datasets. On the other hand, it can be observed that time taken by our algorithm is quite less compared to other methods and justifies the theoretical findings.Algorithms2015-08-2183Article10.3390/a80306806806961999-48932015-08-21doi: 10.3390/a8030680Suman SahaSatya Ghrera<![CDATA[Algorithms, Vol. 8, Pages 669-679: Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators]]>
http://www.mdpi.com/1999-4893/8/3/669
This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution of systems of equations. Without imposing any type of Fréchet differentiability on the operator, a variant using divided differences is also analyzed. A variant of the method using only divided differences is also presented.Algorithms2015-08-2183Article10.3390/a80306696696791999-48932015-08-21doi: 10.3390/a8030669Sergio AmatSonia BusquierConcepción BermúdezÁngel Magreñán<![CDATA[Algorithms, Vol. 8, Pages 656-668: Fifth-Order Iterative Method for Solving Multiple Roots of the Highest Multiplicity of Nonlinear Equation]]>
http://www.mdpi.com/1999-4893/8/3/656
A three-step iterative method with fifth-order convergence as a new modification of Newton’s method was presented. This method is for finding multiple roots of nonlinear equation with unknown multiplicity m whose multiplicity m is the highest multiplicity. Its order of convergence is analyzed and proved. Results for some numerical examples show the efficiency of the new method.Algorithms2015-08-2083Article10.3390/a80306566566681999-48932015-08-20doi: 10.3390/a8030656Juan LiangXiaowu LiZhinan WuMingsheng ZhangLin WangFeng Pan<![CDATA[Algorithms, Vol. 8, Pages 645-655: Local Convergence of an Optimal Eighth Order Method under Weak Conditions]]>
http://www.mdpi.com/1999-4893/8/3/645
We study the local convergence of an eighth order Newton-like method to approximate a locally-unique solution of a nonlinear equation. Earlier studies, such as Chen et al. (2015) show convergence under hypotheses on the seventh derivative or even higher, although only the first derivative and the divided difference appear in these methods. The convergence in this study is shown under hypotheses only on the first derivative. Hence, the applicability of the method is expanded. Finally, numerical examples are also provided to show that our results apply to solve equations in cases where earlier studies cannot apply.Algorithms2015-08-1983Article10.3390/a80306456456551999-48932015-08-19doi: 10.3390/a8030645Ioannis ArgyrosRamandeep BehlS.S. Motsa<![CDATA[Algorithms, Vol. 8, Pages 632-644: Data Fusion Modeling for an RT3102 and Dewetron System Application in Hybrid Vehicle Stability Testing]]>
http://www.mdpi.com/1999-4893/8/3/632
More and more hybrid electric vehicles are driven since they offer such advantages as energy savings and better active safety performance. Hybrid vehicles have two or more power driving systems and frequently switch working condition, so controlling stability is very important. In this work, a two-stage Kalman algorithm method is used to fuse data in hybrid vehicle stability testing. First, the RT3102 navigation system and Dewetron system are introduced. Second, a modeling of data fusion is proposed based on the Kalman filter. Then, this modeling is simulated and tested on a sample vehicle, using Carsim and Simulink software to test the results. The results showed the merits of this modeling.Algorithms2015-08-1283Article10.3390/a80306326326441999-48932015-08-12doi: 10.3390/a8030632Zhibin MiaoHongtian Zhang<![CDATA[Algorithms, Vol. 8, Pages 621-631: One-Bit Quantization and Distributed Detection with an Unknown Scale Parameter]]>
http://www.mdpi.com/1999-4893/8/3/621
We examine a distributed detection problem in a wireless sensor network, where sensor nodes collaborate to detect a Gaussian signal with an unknown change of power, i.e., a scale parameter. Due to power/bandwidth constraints, we consider the case where each sensor quantizes its observation into a binary digit. The binary data are then transmitted through error-prone wireless links to a fusion center, where a generalized likelihood ratio test (GLRT) detector is employed to perform a global decision. We study the design of a binary quantizer based on an asymptotic analysis of the GLRT. Interestingly, the quantization threshold of the quantizer is independent of the unknown scale parameter. Numerical results are included to illustrate the performance of the proposed quantizer and GLRT in binary symmetric channels (BSCs).Algorithms2015-08-1183Article10.3390/a80306216216311999-48932015-08-11doi: 10.3390/a8030621Fei GaoLili GuoHongbin LiJun Fang<![CDATA[Algorithms, Vol. 8, Pages 590-620: An Overview of a Class of Clock Synchronization Algorithms for Wireless Sensor Networks: A Statistical Signal Processing Perspective]]>
http://www.mdpi.com/1999-4893/8/3/590
Recently, wireless sensor networks (WSNs) have drawn great interest due to their outstanding monitoring and management potential in medical, environmental and industrial applications. Most of the applications that employ WSNs demand all of the sensor nodes to run on a common time scale, a requirement that highlights the importance of clock synchronization. The clock synchronization problem in WSNs is inherently related to parameter estimation. The accuracy of clock synchronization algorithms depends essentially on the statistical properties of the parameter estimation algorithms. Recently, studies dedicated to the estimation of synchronization parameters, such as clock offset and skew, have begun to emerge in the literature. The aim of this article is to provide an overview of the state-of-the-art clock synchronization algorithms for WSNs from a statistical signal processing point of view. This article focuses on describing the key features of the class of clock synchronization algorithms that exploit the traditional two-way message (signal) exchange mechanism. Upon introducing the two-way message exchange mechanism, the main clock offset estimation algorithms for pairwise synchronization of sensor nodes are first reviewed, and their performance is compared. The class of fully-distributed clock offset estimation algorithms for network-wide synchronization is then surveyed. The paper concludes with a list of open research problems pertaining to clock synchronization of WSNs.Algorithms2015-08-0683Review10.3390/a80305905906201999-48932015-08-06doi: 10.3390/a8030590Xu WangDaniel JeskeErchin Serpedin<![CDATA[Algorithms, Vol. 8, Pages 573-589: Robust Rank Reduction Algorithm with Iterative Parameter Optimization and Vector Perturbation]]>
http://www.mdpi.com/1999-4893/8/3/573
In dynamic propagation environments, beamforming algorithms may suffer from strong interference, steering vector mismatches, a low convergence speed and a high computational complexity. Reduced-rank signal processing techniques provide a way to address the problems mentioned above. This paper presents a low-complexity robust data-dependent dimensionality reduction based on an iterative optimization with steering vector perturbation (IOVP) algorithm for reduced-rank beamforming and steering vector estimation. The proposed robust optimization procedure jointly adjusts the parameters of a rank reduction matrix and an adaptive beamformer. The optimized rank reduction matrix projects the received signal vector onto a subspace with lower dimension. The beamformer/steering vector optimization is then performed in a reduced dimension subspace. We devise efficient stochastic gradient and recursive least-squares algorithms for implementing the proposed robust IOVP design. The proposed robust IOVP beamforming algorithms result in a faster convergence speed and an improved performance. Simulation results show that the proposed IOVP algorithms outperform some existing full-rank and reduced-rank algorithms with a comparable complexity.Algorithms2015-08-0583Article10.3390/a80305735735891999-48932015-08-05doi: 10.3390/a8030573Peng LiJiao FengRodrigo de Lamare<![CDATA[Algorithms, Vol. 8, Pages 562-572: Modeling Documents with Event Model]]>
http://www.mdpi.com/1999-4893/8/3/562
Currently deep learning has made great breakthroughs in visual and speech processing, mainly because it draws lessons from the hierarchical mode that brain deals with images and speech. In the field of NLP, a topic model is one of the important ways for modeling documents. Topic models are built on a generative model that clearly does not match the way humans write. In this paper, we propose Event Model, which is unsupervised and based on the language processing mechanism of neurolinguistics, to model documents. In Event Model, documents are descriptions of concrete or abstract events seen, heard, or sensed by people and words are objects in the events. Event Model has two stages: word learning and dimensionality reduction. Word learning is to learn semantics of words based on deep learning. Dimensionality reduction is the process that representing a document as a low dimensional vector by a linear mode that is completely different from topic models. Event Model achieves state-of-the-art results on document retrieval tasks.Algorithms2015-08-0483Article10.3390/a80305625625721999-48932015-08-04doi: 10.3390/a8030562Longhui WangGuoguang ZhaoDonghong Sun<![CDATA[Algorithms, Vol. 8, Pages 552-561: Some Improvements to a Third Order Variant of Newton’s Method from Simpson’s Rule]]>
http://www.mdpi.com/1999-4893/8/3/552
In this paper, we present three improvements to a three-point third order variant of Newton’s method derived from the Simpson rule. The first one is a fifth order method using the same number of functional evaluations as the third order method, the second one is a four-point 10th order method and the last one is a five-point 20th order method. In terms of computational point of view, our methods require four evaluations (one function and three first derivatives) to get fifth order, five evaluations (two functions and three derivatives) to get 10th order and six evaluations (three functions and three derivatives) to get 20th order. Hence, these methods have efficiency indexes of 1.495, 1.585 and 1.648, respectively which are better than the efficiency index of 1.316 of the third order method. We test the methods through some numerical experiments which show that the 20th order method is very efficient.Algorithms2015-07-2983Article10.3390/a80305525525611999-48932015-07-29doi: 10.3390/a8030552Diyashvir Babajee<![CDATA[Algorithms, Vol. 8, Pages 541-551: Target Detection Algorithm Based on Two Layers Human Visual System]]>
http://www.mdpi.com/1999-4893/8/3/541
Robust small target detection of low signal-to-noise ratio (SNR) is very important in infrared search and track applications for self-defense or attacks. Due to the complex background, current algorithms have some unsolved issues with false alarm rate. In order to reduce the false alarm rate, an infrared small target detection algorithm based on saliency detection and support vector machine was proposed. Firstly, we detect salient regions that may contain targets with phase spectrum Fourier transform (PFT) approach. Then, target recognition was performed in the salient regions. Experimental results show the proposed algorithm has ideal robustness and efficiency for real infrared small target detection applications.Algorithms2015-07-2983Article10.3390/a80305415415511999-48932015-07-29doi: 10.3390/a8030541Zheng CuiJingli YangShouda JiangChangan Wei<![CDATA[Algorithms, Vol. 8, Pages 529-540: A Parallel Search Strategy Based on Sparse Representation for Infrared Target Tracking]]>
http://www.mdpi.com/1999-4893/8/3/529
A parallel search strategy based on sparse representation (PS-L1 tracker) is proposed in the particle filter framework. To obtain the weights of state particles, target templates are represented linearly with the dictionary of target candidates. Sparse constraints on the coefficient guarantee that only true target candidates can be selected, and the nonnegative entries denote the associate weights of efficient target states. Then the optimal target state can be estimated by the linear combination of above weighted states. In this way, efficient target states are selected simultaneously from all the particles, which we call a parallel search strategy. Experimental results demonstrate excellent performance of the proposed method on challenging infrared images.Algorithms2015-07-2783Article10.3390/a80305295295401999-48932015-07-27doi: 10.3390/a8030529Zhen ShiChang'an WeiPing FuShouda Jiang<![CDATA[Algorithms, Vol. 8, Pages 514-528: On the Accessibility of Newton’s Method under a Hölder Condition on the First Derivative]]>
http://www.mdpi.com/1999-4893/8/3/514
We see how we can improve the accessibility of Newton’s method for approximating a solution of a nonlinear equation in Banach spaces when a center Hölder condition on the first derivative is used to prove its semi-local convergence.Algorithms2015-07-2383Article10.3390/a80305145145281999-48932015-07-23doi: 10.3390/a8030514José EzquerroMiguel Hernández-Verón<![CDATA[Algorithms, Vol. 8, Pages 484-513: Multi-Feedback Interference Cancellation Algorithms for OFDM Systems over Doubly-Selective Channels]]>
http://www.mdpi.com/1999-4893/8/3/484
Orthogonal frequency-division multiplexing (OFDM) systems over rapidly time varying channels may suffer from significant inter-carrier interference (ICI), which destroys the orthogonality between subcarriers and degrades the detection performance. Without sufficient ICI suppression, OFDM systems usually experience an error floor. According to the approximate matched filter bound (AMFB), the error floor in a coded OFDM system is not irreducible. In this work, we introduce novel multiple feedback matched filter (MBMF)-based ICI cancellation receivers. Based on the output of a novel MBMF scheme, the approach employs a multiple ICI cancellation strategy with or without signal-to-interference-plus-noise-ratio (SINR) ordering. The developed schemes can significantly improve the performance and remove the error floor with a negligible complexity increase. Given the multiple cancellation approach, we compare the SINR performance of the MBMF outputs with that employing single feedback and show that the SINR performance with multiple cancellation candidates is improved over that with a single one at practical SNR values. Additionally, for time-varying channels, we exploit partial fast Fourier transform (PFFT) by splitting one OFDM symbol into multiple segments; the channel state is separately estimated by least-squares (LS) methods without inserting more pilots. Simulation results demonstrate the superiority of the proposed methods over serial and block equalizers and the robustness to the Doppler effects compared to conventional single-segment method.Algorithms2015-07-1483Article10.3390/a80304844845131999-48932015-07-14doi: 10.3390/a8030484Peng LiMin ChenLi LiJiao Feng<![CDATA[Algorithms, Vol. 8, Pages 466-483: Conditional Random Fields for Pattern Recognition Applied to Structured Data]]>
http://www.mdpi.com/1999-4893/8/3/466
Pattern recognition uses measurements from an input domain, X, to predict their labels from an output domain, Y. Image analysis is one setting where one might want to infer whether a pixel patch contains an object that is “manmade” (such as a building) or “natural” (such as a tree). Suppose the label for a pixel patch is “manmade”; if the label for a nearby pixel patch is then more likely to be “manmade” there is structure in the output domain that can be exploited to improve pattern recognition performance. Modeling P(X) is difficult because features between parts of the model are often correlated. Therefore, conditional random fields (CRFs) model structured data using the conditional distribution P(Y|X = x), without specifying a model for P(X), and are well suited for applications with dependent features. This paper has two parts. First, we overview CRFs and their application to pattern recognition in structured problems. Our primary examples are image analysis applications in which there is dependence among samples (pixel patches) in the output domain. Second, we identify research topics and present numerical examples.Algorithms2015-07-1483Review10.3390/a80304664664831999-48932015-07-14doi: 10.3390/a8030466Tom BurrAlexei Skurikhin<![CDATA[Algorithms, Vol. 8, Pages 459-465: Solving the (n2 − 1)-Puzzle with 8/3 n3 Expected Moves]]>
http://www.mdpi.com/1999-4893/8/3/459
It is shown that the greedy algorithm for the \((n^2-1)\)-puzzle makes \(\tfrac{8}{3}n^3 +O(n^2)\) expected moves. This analysis is verified experimentally on 10,000 random instances each of the \((n^2-1)\)-puzzle for \(4 \leq n \leq 200\).Algorithms2015-07-1083Article10.3390/a80304594594651999-48932015-07-10doi: 10.3390/a8030459Ian Parberry<![CDATA[Algorithms, Vol. 8, Pages 435-458: A Benchmarking Algorithm to Determine Minimum Aggregation Delay for Data Gathering Trees and an Analysis of the Diameter-Aggregation Delay Tradeoff]]>
http://www.mdpi.com/1999-4893/8/3/435
Aggregation delay is the minimum number of time slots required to aggregate data along the edges of a data gathering tree (DG tree) spanning all the nodes in a wireless sensor network (WSN). We propose a benchmarking algorithm to determine the minimum possible aggregation delay for DG trees in a WSN. We assume the availability of a sufficient number of unique CDMA (Code Division Multiple Access) codes for the intermediate nodes to simultaneously aggregate data from their child nodes if the latter are ready with the data. An intermediate node has to still schedule non-overlapping time slots to sequentially aggregate data from its own child nodes (one time slot per child node). We show that the minimum aggregation delay for a DG tree depends on the underlying design choices (bottleneck node-weight based or bottleneck link-weight based) behind its construction. We observe the bottleneck node-weight based DG trees incur a smaller diameter and a larger number of child nodes per intermediate node; whereas, the bottleneck link-weight based DG trees incur a larger diameter and a much lower number of child nodes per intermediate node. As a result, we observe a complex diameter-aggregation delay tradeoff for data gathering trees in WSNs.Algorithms2015-07-1083Article10.3390/a80304354354581999-48932015-07-10doi: 10.3390/a8030435Natarajan Meghanathan<![CDATA[Algorithms, Vol. 8, Pages 424-434: Multi-Objective Design Optimization of an Over-Constrained Flexure-Based Amplifier]]>
http://www.mdpi.com/1999-4893/8/3/424
The optimizing design for enhancement of the micro performance of manipulator based on analytical models is investigated in this paper. By utilizing the established uncanonical linear homogeneous equations, the quasi-static analytical model of the micro-manipulator is built, and the theoretical calculation results are tested by FEA simulations. To provide a theoretical basis for a micro-manipulator being used in high-precision engineering applications, this paper investigates the modal property based on the analytical model. Based on the finite element method, with multipoint constraint equations, the model is built and the results have a good match with the simulation. The following parametric influences studied show that the influences of other objectives on one objective are complicated. Consequently, the multi-objective optimization by the derived analytical models is carried out to find out the optimal solutions of the manipulator. Besides the inner relationships among these design objectives during the optimization process are discussed.Algorithms2015-07-0883Article10.3390/a80304244244341999-48932015-07-08doi: 10.3390/a8030424Yuan NiZongquan DengJunbao LiXiang WuLong Li<![CDATA[Algorithms, Vol. 8, Pages 415-423: A Quartically Convergent Jarratt-Type Method for Nonlinear System of Equations]]>
http://www.mdpi.com/1999-4893/8/3/415
In this work, we propose a new fourth-order Jarratt-type method for solving systems of nonlinear equations. The local convergence order of the method is proven analytically. Finally, we validate our results via some numerical experiments including an application to the Chandrashekar integral equations.Algorithms2015-07-0683Article10.3390/a80304154154231999-48932015-07-06doi: 10.3390/a8030415Mohammad GhorbanzadehFazlollah Soleymani<![CDATA[Algorithms, Vol. 8, Pages 407-414: Implementation of a Parallel Algorithm Based on a Spark Cloud Computing Platform]]>
http://www.mdpi.com/1999-4893/8/3/407
Parallel algorithms, such as the ant colony algorithm, take a long time when solving large-scale problems. In this paper, the MAX-MIN Ant System algorithm (MMAS) is parallelized to solve Traveling Salesman Problem (TSP) based on a Spark cloud computing platform. We combine MMAS with Spark MapReduce to execute the path building and the pheromone operation in a distributed computer cluster. To improve the precision of the solution, local optimization strategy 2-opt is adapted in MMAS. The experimental results show that Spark has a very great accelerating effect on the ant colony algorithm when the city scale of TSP or the number of ants is relatively large.Algorithms2015-07-0383Article10.3390/a80304074074141999-48932015-07-03doi: 10.3390/a8030407Longhui WangYong WangYudong Xie<![CDATA[Algorithms, Vol. 8, Pages 395-406: Algorithms for Computerized Fetal Heart Rate Diagnosis with Direct Reporting]]>
http://www.mdpi.com/1999-4893/8/3/395
Aims: Since pattern classification of fetal heart rate (FHR) was subjective and enlarged interobserver difference, objective FHR analysis was achieved with computerized FHR diagnosis. Methods: The computer algorithm was composed of an experts’ knowledge system, including FHR analysis and FHR score calculation, and also of an objective artificial neural network system with software. In addition, a FHR frequency spectrum was studied to detect ominous sinusoidal FHR and the loss of baseline variability related to fetal brain damage. The algorithms were installed in a central-computerized automatic FHR monitoring system, which gave the diagnosis rapidly and directly to the attending doctor. Results: Clinically perinatal mortality decreased significantly and no cerebral palsy developed after introduction of the centralized system. Conclusion: The automatic multichannel FHR monitoring system improved the monitoring, increased the objectivity of FHR diagnosis and promoted clinical results.Algorithms2015-06-2983Review10.3390/a80303953954061999-48932015-06-29doi: 10.3390/a8030395Kazuo MaedaYasuaki NoguchiMasaji UtsuTakashi Nagassawa<![CDATA[Algorithms, Vol. 8, Pages 380-394: Improving CLOPE’s Profit Value and Stability with an Optimized Agglomerative Approach]]>
http://www.mdpi.com/1999-4893/8/3/380
CLOPE (Clustering with sLOPE) is a simple and fast histogram-based clustering algorithm for categorical data. However, given the same data set with the same input parameter, the clustering results by this algorithm would possibly be different if the transactions are input in a different sequence. In this paper, a hierarchical clustering framework is proposed as an extension of CLOPE to generate stable and satisfactory clustering results based on an optimized agglomerative merge process. The new clustering profit is defined as the merge criteria and the cluster graph structure is proposed to optimize the merge iteration process. The experiments conducted on two datasets both demonstrate that the agglomerative approach achieves stable clustering results with a better profit value, but costs much more time due to the worse complexity.Algorithms2015-06-2683Article10.3390/a80303803803941999-48932015-06-26doi: 10.3390/a8030380Yefeng LiJiajin LeMei Wang<![CDATA[Algorithms, Vol. 8, Pages 366-379: Identification of Dual-Rate Sampled Hammerstein Systems with a Piecewise-Linear Nonlinearity Using the Key Variable Separation Technique]]>
http://www.mdpi.com/1999-4893/8/3/366
The identification difficulties for a dual-rate Hammerstein system lie in two aspects. First, the identification model of the system contains the products of the parameters of the nonlinear block and the linear block, and a standard least squares method cannot be directly applied to the model; second, the traditional single-rate discrete-time Hammerstein model cannot be used as the identification model for the dual-rate sampled system. In order to solve these problems, by combining the polynomial transformation technique with the key variable separation technique, this paper converts the Hammerstein system into a dual-rate linear regression model about all parameters (linear-in-parameter model) and proposes a recursive least squares algorithm to estimate the parameters of the dual-rate system. The simulation results verify the effectiveness of the proposed algorithm.Algorithms2015-06-2483Article10.3390/a80303663663791999-48932015-06-24doi: 10.3390/a8030366Ying-Ying WangXiang-Dong WangDong-Qing Wang<![CDATA[Algorithms, Vol. 8, Pages 336-365: MAKHA—A New Hybrid Swarm Intelligence Global Optimization Algorithm]]>
http://www.mdpi.com/1999-4893/8/2/336
The search for efficient and reliable bio-inspired optimization methods continues to be an active topic of research due to the wide application of the developed methods. In this study, we developed a reliable and efficient optimization method via the hybridization of two bio-inspired swarm intelligence optimization algorithms, namely, the Monkey Algorithm (MA) and the Krill Herd Algorithm (KHA). The hybridization made use of the efficient steps in each of the two original algorithms and provided a better balance between the exploration/diversification steps and the exploitation/intensification steps. The new hybrid algorithm, MAKHA, was rigorously tested with 27 benchmark problems and its results were compared with the results of the two original algorithms. MAKHA proved to be considerably more reliable and more efficient in tested problems.Algorithms2015-06-1982Article10.3390/a80203363363651999-48932015-06-19doi: 10.3390/a8020336Ahmed KhalilSeif-Eddeen FateenAdrián Bonilla-Petriciolet<![CDATA[Algorithms, Vol. 8, Pages 321-335: Time Domain Simulation of Sound Waves Using Smoothed Particle Hydrodynamics Algorithm with Artificial Viscosity]]>
http://www.mdpi.com/1999-4893/8/2/321
Smoothed particle hydrodynamics (SPH), as a Lagrangian, meshfree method, is supposed to be useful in solving acoustic problems, such as combustion noise, bubble acoustics, etc., and has been gradually used in sound wave computation. However, unphysical oscillations in the sound wave simulation cannot be ignored. In this paper, an artificial viscosity term is added into the standard SPH algorithm used for solving linearized acoustic wave equations. SPH algorithms with or without artificial viscosity are both built to compute sound propagation and interference in the time domain. Then, the effects of the smoothing kernel function, particle spacing and Courant number on the SPH algorithms of sound waves are discussed. After comparing SPH simulation results with theoretical solutions, it is shown that the result of the SPH algorithm with the artificial viscosity term added attains good agreement with the theoretical solution by effectively reducing unphysical oscillations. In addition, suitable computational parameters of SPH algorithms are proposed through analyzing the sound pressure errors for simulating sound waves.Algorithms2015-06-1782Article10.3390/a80203213213351999-48932015-06-17doi: 10.3390/a8020321Xu LiTao ZhangYong Zhang<![CDATA[Algorithms, Vol. 8, Pages 309-320: An Optimal Eighth-Order Derivative-Free Family of Potra-Pták’s Method]]>
http://www.mdpi.com/1999-4893/8/2/309
In this paper, we present a new three-step derivative-free family based on Potra-Pták’s method for solving nonlinear equations numerically. In terms of computational cost, each member of the proposed family requires only four functional evaluations per full iteration to achieve optimal eighth-order convergence. Further, computational results demonstrate that the proposed methods are highly efficient as compared with many well-known methods.Algorithms2015-06-1582Article10.3390/a80203093093201999-48932015-06-15doi: 10.3390/a8020309Munish KansalVinay KanwarSaurabh Bhatia<![CDATA[Algorithms, Vol. 8, Pages 292-308: Training Artificial Neural Networks by a Hybrid PSO-CS Algorithm]]>
http://www.mdpi.com/1999-4893/8/2/292
Presenting a satisfactory and efficient training algorithm for artificial neural networks (ANN) has been a challenging task in the supervised learning area. Particle swarm optimization (PSO) is one of the most widely used algorithms due to its simplicity of implementation and fast convergence speed. On the other hand, Cuckoo Search (CS) algorithm has been proven to have a good ability for finding the global optimum; however, it has a slow convergence rate. In this study, a hybrid algorithm based on PSO and CS is proposed to make use of the advantages of both PSO and CS algorithms. The proposed hybrid algorithm is employed as a new training method for feedforward neural networks (FNNs). To investigate the performance of the proposed algorithm, two benchmark problems are used and the results are compared with those obtained from FNNs trained by original PSO and CS algorithms. The experimental results show that the proposed hybrid algorithm outperforms both PSO and CS in training FNNs.Algorithms2015-06-1182Article10.3390/a80202922923081999-48932015-06-11doi: 10.3390/a8020292Jeng-Fung ChenQuang DoHo-Nien Hsieh<![CDATA[Algorithms, Vol. 8, Pages 280-291: Model Equivalence-Based Identification Algorithm for Equation-Error Systems with Colored Noise]]>
http://www.mdpi.com/1999-4893/8/2/280
For equation-error autoregressive (EEAR) systems, this paper proposes an identification algorithm by means of the model equivalence transformation. The basic idea is to eliminate the autoregressive term in the model using the model transformation, to estimate the parameters of the converted system and further to compute the parameter estimates of the original system using the comparative coefficient way and the model equivalence principle. For comparison, the recursive generalized least squares algorithm is given simply. The simulation results verify that the proposed algorithm is effective and can produce more accurate parameter estimates.Algorithms2015-06-0282Article10.3390/a80202802802911999-48932015-06-02doi: 10.3390/a8020280Dandan MengFeng Ding<![CDATA[Algorithms, Vol. 8, Pages 271-279: Dynamics and Fractal Dimension of Steffensen-Type Methods]]>
http://www.mdpi.com/1999-4893/8/2/271
In this paper, the dynamical behavior of different optimal iterative schemes for solving nonlinear equations with increasing order, is studied. The tendency of the complexity of the Julia set is analyzed and referred to the fractal dimension. In fact, this fractal dimension can be shown to be a powerful tool to compare iterative schemes that estimate the solution of a nonlinear equation. Based on the box-counting algorithm, several iterative derivative-free methods of different convergence orders are compared.Algorithms2015-06-0182Article10.3390/a80202712712791999-48932015-06-01doi: 10.3390/a8020271Francisco ChicharroAlicia CorderoJuan Torregrosa<![CDATA[Algorithms, Vol. 8, Pages 248-270: On String Matching with Mismatches]]>
http://www.mdpi.com/1999-4893/8/2/248
In this paper, we consider several variants of the pattern matching with mismatches problem. In particular, given a text \(T=t_1 t_2\cdots t_n\) and a pattern \(P=p_1p_2\cdots p_m\), we investigate the following problems: (1) pattern matching with mismatches: for every \(i, 1\leq i \leq n-m+1\) output, the distance between \(P\) and \(t_i t_{i+1}\cdots t_{i+m-1}\); and (2) pattern matching with \(k\) mismatches: output those positions \(i\) where the distance between \(P\) and \(t_i t_{i+1}\cdots t_{i+m-1}\) is less than a given threshold \(k\). The distance metric used is the Hamming distance. We present some novel algorithms and techniques for solving these problems. We offer deterministic, randomized and approximation algorithms. We consider variants of these problems where there could be wild cards in either the text or the pattern or both. We also present an experimental evaluation of these algorithms. The source code is available at http://www.engr.uconn.edu/\(\sim\)man09004/kmis.zip.Algorithms2015-05-2682Article10.3390/a80202482482701999-48932015-05-26doi: 10.3390/a8020248Marius NicolaeSanguthevar Rajasekaran<![CDATA[Algorithms, Vol. 8, Pages 234-247: An Optimization Clustering Algorithm Based on Texture Feature Fusion for Color Image Segmentation]]>
http://www.mdpi.com/1999-4893/8/2/234
We introduce a multi-feature optimization clustering algorithm for color image segmentation. The local binary pattern, the mean of the min-max difference, and the color components are combined as feature vectors to describe the magnitude change of grey value and the contrastive information of neighbor pixels. In clustering stage, it gets the initial clustering center and avoids getting into local optimization by adding mutation operator of genetic algorithm to particle swarm optimization. Compared with well-known methods, the proposed method has an overall better segmentation performance and can segment image more accurately by evaluating the ratio of misclassification.Algorithms2015-05-2282Article10.3390/a80202342342471999-48932015-05-22doi: 10.3390/a8020234Gaihua WangYang LiuCaiquan Xiong<![CDATA[Algorithms, Vol. 8, Pages 224-233: Numerical Solution of Turbulence Problems by Solving Burgers’ Equation]]>
http://www.mdpi.com/1999-4893/8/2/224
In this work we generate the numerical solutions of Burgers’ equation by applying the Crank-Nicholson method and different schemes for solving nonlinear systems, instead of using Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. The method is analyzed on two test problems in order to check its efficiency on different kinds of initial conditions. Numerical solutions as well as exact solutions for different values of viscosity are calculated, concluding that the numerical results are very close to the exact solution.Algorithms2015-05-0882Article10.3390/a80202242242331999-48932015-05-08doi: 10.3390/a8020224Alicia CorderoAntonio FranquesJuan Torregrosa