Algorithms, Volume 11, Issue 1 (January 2018) – 11 articles

The Small Set Expansion Hypothesis is a conjecture which roughly states that it is NP-hard to distinguish between a graph with a small subset of vertices whose (edge) expansion is almost zero and one in which all small subsets of vertices have expansion almost one. In this work, we prove conditional inapproximability results with essentially optimal ratios for the following graph problems based on this hypothesis: Maximum Edge Biclique, Maximum Balanced Biclique, Minimum k-Cut and Densest At-Least-k-Subgraph. Our hardness results for the two biclique problems are proved by combining a technique developed by Raghavendra, Steurer and Tulsiani to avoid locality of gadget reductions with a generalization of Bansal and Khot’s long code test whereas our results for Minimum k-Cut and Densest At-Least-k-Subgraph are shown via elementary reductions. Full article

Variation in the format and classification requirements for remote sensing data makes establishing a standard remote sensing sample dataset difficult. As a result, few remote sensing deep neural network models have been widely accepted. We propose a hybrid deep neural network model based on a convolutional auto-encoder and a complementary convolutional neural network to solve this problem. The convolutional auto-encoder supports feature extraction and data dimension reduction of remote sensing data. The extracted features are input into the convolutional neural network and subsequently classified. Experimental results show that in the proposed model, the classification accuracy increases from 0.916 to 0.944, compared to a traditional convolutional neural network model; furthermore, the number of training runs is reduced from 40,000 to 22,000, and the number of labelled samples can be reduced by more than half, all while ensuring a classification accuracy of no less than 0.9, which suggests the effectiveness and feasibility of the proposed model. Full article

In this article we suggest a randomized algorithm for the LQR (Linear Quadratic Regulator) optimal-control problem via static-output-feedback. The suggested algorithm is based on the recently introduced randomized optimization method called the Ray-Shooting Method that efficiently solves the global minimization problem of continuous functions over compact non-convex unconnected regions. The algorithm presented here is a randomized algorithm with a proof of convergence in probability. Its practical implementation has good performance in terms of the quality of controllers obtained and the percentage of success. Full article

In order to improve the control precision and robustness of the existing proportion integration differentiation (PID) controller of a 3-Revolute–Revolute–Revolute (3-RRR) parallel robot, a variable PID parameter controller optimized by a genetic algorithm controller is proposed in this paper. Firstly, the inverse kinematics model of the 3-RRR parallel robot was established according to the vector method, and the motor conversion matrix was deduced. Then, the error square integral was chosen as the fitness function, and the genetic algorithm controller was designed. Finally, the control precision of the new controller was verified through the simulation model of the 3-RRR planar parallel robot—built in SimMechanics—and the robustness of the new controller was verified by adding interference. The results show that compared with the traditional PID controller, the new controller designed in this paper has better control precision and robustness, which provides the basis for practical application. Full article

The perceptual hash algorithm is a technique to authenticate the integrity of images. While a few scholars have worked on mono-spectral image perceptual hashing, there is limited research on multispectral image perceptual hashing. In this paper, we propose a perceptual hash algorithm for the content authentication of a multispectral remote sensing image based on the synthetic characteristics of each band: firstly, the multispectral remote sensing image is preprocessed with band clustering and grid partition; secondly, the edge feature of the band subsets is extracted by band fusion-based edge feature extraction; thirdly, the perceptual feature of the same region of the band subsets is compressed and normalized to generate the perceptual hash value. The authentication procedure is achieved via the normalized Hamming distance between the perceptual hash value of the recomputed perceptual hash value and the original hash value. The experiments indicated that our proposed algorithm is robust compared to content-preserved operations and it efficiently authenticates the integrity of multispectral remote sensing images. Full article

In this paper, we investigate multiple-attribute decision-making (MADM) with Pythagorean 2-tuple linguistic numbers (P2TLNs). Then, we combine the weighted Bonferroni mean (WBM) operator and weighted geometric Bonferroni mean (WGBM) operator with P2TLNs to propose the Pythagorean 2-tuple linguistic WBM (P2TLWBM) operator and Pythagorean 2-tuple linguistic WGBM (P2TLWGBM) operator; MADM methods are then developed based on these two operators. Finally, a practical example for green supplier selection is given to verify the developed approach and to demonstrate its practicality and effectiveness. Full article

Recently, inspired by the power of deep learning, convolution neural networks can produce fantastic images at the pixel level. However, a significant limiting factor for previous approaches is that they focus on some simple datasets such as faces and bedrooms. In this paper, we propose a multiscale deep neural network to transform sketches into Chinese paintings. To synthesize more realistic imagery, we train the generative network by using both L1 loss and adversarial loss. Additionally, users can control the process of the synthesis since the generative network is feed-forward. This network can also be treated as neural style transfer by adding an edge detector. Furthermore, additional experiments on image colorization and image super-resolution demonstrate the universality of our proposed approach. Full article

Seeding heuristics are the most widely used strategies to speed up sequence alignment in bioinformatics. Such strategies are most successful if they are calibrated, so that the speed-versus-accuracy trade-off can be properly tuned. In the widely used case of read mapping, it has been so far impossible to predict the success rate of competing seeding strategies for lack of a theoretical framework. Here, we present an approach to estimate such quantities based on the theory of analytic combinatorics. The strategy is to specify a combinatorial construction of reads where the seeding heuristic fails, translate this specification into a generating function using formal rules, and finally extract the probabilities of interest from the singularities of the generating function. The generating function can also be used to set up a simple recurrence to compute the probabilities with greater precision. We use this approach to construct simple estimators of the success rate of the seeding heuristic under different types of sequencing errors, and we show that the estimates are accurate in practical situations. More generally, this work shows novel strategies based on analytic combinatorics to compute probabilities of interest in bioinformatics. Full article

In this article, we expand the dual generalized weighted BM (DGWBM) and dual generalized weighted geometric Bonferroni mean (DGWGBM) operator with single valued neutrosophic numbers (SVNNs) to propose the dual generalized single-valued neutrosophic number WBM (DGSVNNWBM) operator and dual generalized single-valued neutrosophic numbers WGBM (DGSVNNWGBM) operator. Then, the multiple attribute decision making (MADM) methods are proposed with these operators. In the end, we utilize an applicable example for strategic suppliers selection to prove the proposed methods. Full article

Investigation of the interaction of electromagnetic radiation with molecular systems provides most of the information on their structure and properties. Interpretation of experimental data is directly determined by the knowledge of the structure of energy levels and its change in the transition of these systems to an excited state. A key task of the methods for calculating the molecular orbitals of excited states is to accurately describe the emerging vacancies of the molecular core, leading to radial relaxation of the electron density. We propose an iterative scheme for solving a system of coupled integro-differential equations for obtaining molecular orbitals of electron configurations with excited/ionized deep and subvalent shells in a single-center representation. The numerical procedure of the iterative scheme is reduced to solving a boundary value problem based on a combination of the three-point difference scheme of Numerov and Thomas algorithm. To increase the rate of convergence of the computational procedure, an accurate account is taken of the behavior of the electron density near the nuclei of the molecular system. The realization of the algorithm of the computational scheme is considered on the example of a diatomic hydrogen fluoride molecule. The energy characteristics of the ground and ionized states of the molecule are estimated, and also the spatial distribution of the electron density is presented for the example of the σ-symmetry shell. Full article