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## Algorithms, Volume 5, Issue 1 (March 2012), Pages 1-175

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Open AccessArticle An Integer Programming Approach to Solving Tantrix on Fixed Boards
Algorithms 2012, 5(1), 158-175; https://doi.org/10.3390/a5010158
Received: 15 December 2011 / Revised: 9 March 2012 / Accepted: 14 March 2012 / Published: 22 March 2012
Cited by 1 | PDF Full-text (6813 KB)
Abstract
Tantrix (Tantrix R ⃝ is a registered trademark of Colour of Strategy Ltd. in New Zealand, and of TANTRIX JAPAN in Japan, respectively, under the license of M. McManaway, the inventor.) is a puzzle to make a loop by connecting lines drawn on
Tantrix (Tantrix R ⃝ is a registered trademark of Colour of Strategy Ltd. in New Zealand, and of TANTRIX JAPAN in Japan, respectively, under the license of M. McManaway, the inventor.) is a puzzle to make a loop by connecting lines drawn on hexagonal tiles, and the objective of this research is to solve it by a computer. For this purpose, we first give a problem setting of solving Tantrix as making a loop on a given fixed board. We then formulate it as an integer program by describing the rules of Tantrix as its constraints, and solve it by a mathematical programming solver to have a solution. As a result, we establish a formulation that can solve Tantrix of moderate size, and even when the solutions are invalid only by elementary constraints, we achieved it by introducing additional constraints and re-solve it. By this approach we succeeded to solve Tantrix of size up to 60. Full article
Open AccessArticle Any Monotone Function Is Realized by Interlocked Polygons
Algorithms 2012, 5(1), 148-157; https://doi.org/10.3390/a5010148
Received: 15 November 2011 / Revised: 13 March 2012 / Accepted: 14 March 2012 / Published: 19 March 2012
Cited by 1 | PDF Full-text (2190 KB)
Abstract
Suppose there is a collection of n simple polygons in the plane, none of which overlap each other. The polygons are interlocked if no subset can be separated arbitrarily far from the rest. It is natural to ask the characterization of the subsets
Suppose there is a collection of n simple polygons in the plane, none of which overlap each other. The polygons are interlocked if no subset can be separated arbitrarily far from the rest. It is natural to ask the characterization of the subsets that makes the set of interlocked polygons free (not interlocked). This abstracts the essence of a kind of sliding block puzzle. We show that any monotone Boolean function ƒ on n variables can be described by m = O(n) interlocked polygons. We also show that the decision problem that asks if given polygons are interlocked is PSPACE-complete. Full article
Open AccessArticle A Semi-Preemptive Computational Service System with Limited Resources and Dynamic Resource Ranking
Algorithms 2012, 5(1), 113-147; https://doi.org/10.3390/a5010113
Received: 13 February 2012 / Revised: 6 March 2012 / Accepted: 6 March 2012 / Published: 14 March 2012
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Abstract
In this paper, we integrate a grid system and a wireless network to present a convenient computational service system, called the Semi-Preemptive Computational Service system (SePCS for short), which provides users with a wireless access environment and through which a user can share
In this paper, we integrate a grid system and a wireless network to present a convenient computational service system, called the Semi-Preemptive Computational Service system (SePCS for short), which provides users with a wireless access environment and through which a user can share his/her resources with others. In the SePCS, each node is dynamically given a score based on its CPU level, available memory size, current length of waiting queue, CPU utilization and bandwidth. With the scores, resource nodes are classified into three levels. User requests based on their time constraints are also classified into three types. Resources of higher levels are allocated to more tightly constrained requests so as to increase the total performance of the system. To achieve this, a resource broker with the Semi-Preemptive Algorithm (SPA) is also proposed. When the resource broker cannot find suitable resources for the requests of higher type, it preempts the resource that is now executing a lower type request so that the request of higher type can be executed immediately. The SePCS can be applied to a Vehicular Ad Hoc Network (VANET), users of which can then exploit the convenient mobile network services and the wireless distributed computing. As a result, the performance of the system is higher than that of the tested schemes. Full article
(This article belongs to the Special Issue Data Compression, Communication and Processing)
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Open AccessArticle Successive Standardization of Rectangular Arrays
Algorithms 2012, 5(1), 98-112; https://doi.org/10.3390/a5010098
Received: 17 November 2011 / Revised: 20 February 2012 / Accepted: 20 February 2012 / Published: 29 February 2012
Cited by 1 | PDF Full-text (804 KB)
Abstract
In this note we illustrate and develop further with mathematics and examples, the work on successive standardization (or normalization) that is studied earlier by the same authors in [1] and [2]. Thus, we deal with successive iterations applied to rectangular arrays of numbers,
In this note we illustrate and develop further with mathematics and examples, the work on successive standardization (or normalization) that is studied earlier by the same authors in [1] and [2]. Thus, we deal with successive iterations applied to rectangular arrays of numbers, where to avoid technical difficulties an array has at least three rows and at least three columns. Without loss, an iteration begins with operations on columns: first subtract the mean of each column; then divide by its standard deviation. The iteration continues with the same two operations done successively for rows. These four operations applied in sequence completes one iteration. One then iterates again, and again, and again, ... In [1] it was argued that if arrays are made up of real numbers, then the set for which convergence of these successive iterations fails has Lebesgue measure 0. The limiting array has row and column means 0, row and column standard deviations 1. A basic result on convergence given in [1] is true, though the argument in [1] is faulty. The result is stated in the form of a theorem here, and the argument for the theorem is correct. Moreover, many graphics given in [1] suggest that except for a set of entries of any array with Lebesgue measure 0, convergence is very rapid, eventually exponentially fast in the number of iterations. Because we learned this set of rules from Bradley Efron, we call it “Efron’s algorithm”. More importantly, the rapidity of convergence is illustrated by numerical examples. Full article
(This article belongs to the Special Issue Data Compression, Communication and Processing)
Open AccessArticle Visualization, Band Ordering and Compression of Hyperspectral Images
Algorithms 2012, 5(1), 76-97; https://doi.org/10.3390/a5010076
Received: 16 November 2011 / Revised: 18 January 2012 / Accepted: 30 January 2012 / Published: 20 February 2012
Cited by 11 | PDF Full-text (904 KB) | HTML Full-text | XML Full-text
Abstract
Air-borne and space-borne acquired hyperspectral images are used to recognize objects and to classify materials on the surface of the earth. The state of the art compressor for lossless compression of hyperspectral images is the Spectral oriented Least SQuares (SLSQ) compressor (see [1–7]).
Air-borne and space-borne acquired hyperspectral images are used to recognize objects and to classify materials on the surface of the earth. The state of the art compressor for lossless compression of hyperspectral images is the Spectral oriented Least SQuares (SLSQ) compressor (see [1–7]). In this paper we discuss hyperspectral image compression: we show how to visualize each band of a hyperspectral image and how this visualization suggests that an appropriate band ordering can lead to improvements in the compression process. In particular, we consider two important distance measures for band ordering: Pearson’s Correlation and Bhattacharyya distance, and report on experimental results achieved by a Java-based implementation of SLSQ. Full article
(This article belongs to the Special Issue Data Compression, Communication and Processing)
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Open AccessArticle Application of Genetic Control with Adaptive Scaling Scheme to Signal Acquisition in Global Navigation Satellite System Receiver
Algorithms 2012, 5(1), 56-75; https://doi.org/10.3390/a5010056
Received: 10 December 2011 / Revised: 6 February 2012 / Accepted: 9 February 2012 / Published: 17 February 2012
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Abstract
This paper presents a genetic-based control scheme that not only utilizes evolutionary characteristics to find the signal acquisition parameters, but also employs an adaptive scheme to control the search space and avoid the genetic control converging to local optimal value so as to
This paper presents a genetic-based control scheme that not only utilizes evolutionary characteristics to find the signal acquisition parameters, but also employs an adaptive scheme to control the search space and avoid the genetic control converging to local optimal value so as to acquire the desired signal precisely and rapidly. Simulations and experiment results show that the proposed method can improve the precision of signal parameters and take less signal acquisition time than traditional serial search methods for global navigation satellite system (GNSS) signals. Full article
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Open AccessArticle A Note on Sequence Prediction over Large Alphabets
Algorithms 2012, 5(1), 50-55; https://doi.org/10.3390/a5010050
Received: 14 November 2011 / Revised: 11 February 2012 / Accepted: 13 February 2012 / Published: 17 February 2012
Cited by 1 | PDF Full-text (153 KB)
Abstract
Building on results from data compression, we prove nearly tight bounds on how well sequences of length n can be predicted in terms of the size σ of the alphabet and the length k of the context considered when making predictions. We compare
Building on results from data compression, we prove nearly tight bounds on how well sequences of length n can be predicted in terms of the size σ of the alphabet and the length k of the context considered when making predictions. We compare the performance achievable by an adaptive predictor with no advance knowledge of the sequence, to the performance achievable by the optimal static predictor using a table listing the frequency of each (k + 1)-tuple in the sequence. We show that, if the elements of the sequence are chosen uniformly at random, then an adaptive predictor can compete in the expected case if k ≤ logσ n – 3 – ε, for a constant ε > 0, but not if k ≥ logσ n. Full article
(This article belongs to the Special Issue Data Compression, Communication and Processing)
Open AccessArticle Standard and Specific Compression Techniques for DNA Microarray Images
Algorithms 2012, 5(1), 30-49; https://doi.org/10.3390/a5010030
Received: 14 November 2011 / Revised: 22 January 2012 / Accepted: 22 January 2012 / Published: 14 February 2012
Cited by 2 | PDF Full-text (650 KB)
Abstract
We review the state of the art in DNA microarray image compression and provide original comparisons between standard and microarray-specific compression techniques that validate and expand previous work. First, we describe the most relevant approaches published in the literature and classify them according
We review the state of the art in DNA microarray image compression and provide original comparisons between standard and microarray-specific compression techniques that validate and expand previous work. First, we describe the most relevant approaches published in the literature and classify them according to the stage of the typical image compression process where each approach makes its contribution, and then we summarize the compression results reported for these microarray-specific image compression schemes. In a set of experiments conducted for this paper, we obtain new results for several popular image coding techniques that include the most recent coding standards. Prediction-based schemes CALIC and JPEG-LS are the best-performing standard compressors, but are improved upon by the best microarray-specific technique, Battiato’s CNN-based scheme. Full article
(This article belongs to the Special Issue Data Compression, Communication and Processing)
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Open AccessArticle How to Solve the Torus Puzzle
Algorithms 2012, 5(1), 18-29; https://doi.org/10.3390/a5010018
Received: 27 December 2011 / Revised: 30 December 2011 / Accepted: 30 December 2011 / Published: 13 January 2012
Cited by 2 | PDF Full-text (191 KB)
Abstract
In this paper, we consider the following sliding puzzle called torus puzzle. In an m by n board, there are mn pieces numbered from 1 to mn. Initially, the pieces are placed in ascending order. Then they are scrambled by rotating the
In this paper, we consider the following sliding puzzle called torus puzzle. In an m by n board, there are mn pieces numbered from 1 to mn. Initially, the pieces are placed in ascending order. Then they are scrambled by rotating the rows and columns without the player’s knowledge. The objective of the torus puzzle is to rearrange the pieces in ascending order by rotating the rows and columns. We provide a solution to this puzzle. In addition, we provide lower and upper bounds on the number of steps for solving the puzzle. Moreover, we consider a variant of the torus puzzle in which each piece is colored either black or white, and we present a hardness result for solving it. Full article
Open AccessArticle Compression-Based Tools for Navigation with an Image Database
Algorithms 2012, 5(1), 1-17; https://doi.org/10.3390/a5010001
Received: 23 August 2011 / Revised: 6 December 2011 / Accepted: 19 December 2011 / Published: 10 January 2012
Cited by 5 | PDF Full-text (2242 KB) | HTML Full-text | XML Full-text
Abstract
We present tools that can be used within a larger system referred to as a passive assistant. The system receives information from a mobile device, as well as information from an image database such as Google Street View, and employs image