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On Evolutionary Algorithms for Large Cliques in Random graphs

INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS 2011年第S11期22卷 53-60页

作者： Javidi, Mohammad M. Mehrabi, Saeed Shahid Bahonar Univ Kerman Dept Comp Sci Kerman Iran

The maximum clique problem (MCP) is an old NP-complete problem which has been frequently used for delivering the NP-completeness of many other problems with respect to computational complexity literature. In this paper, we give a heuristic based genetic algorithm for solving this problem. By incorporating a heuristic into the crossover operator, we speed up the convergence rate of our algorithm - GACP (genetic algorithm for clique problem). GACP has been tested on a variety of challenging benchmarks including DIMACS instances and compared with two recently efficient algorithms. Experimental results show that GACP not only competes consistently with these algorithms but also performed well at solving the maximum clique problem.

关键词： algorithmic graph theory Combinatorial Optimization Maximum Clique Problem

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A New Approach to graph Recognition and Applications to Distance-Hereditary graphs

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Journal of Computer Science & Technology 2009年第3期24卷 517-533页

作者： Shin-ichi Nakano Ryuhei Uehara Takeaki Uno Department of Computer Science Faculty of EngineeringGunma UniversityGunma 376-8515Japan School of Information Science Japan Advanced Institute of Science and TechnologyIshikawa 923-1292Japan National Institute of Informatics Tokyo 101-8430Japan

Algorithms used in data mining and bioinformatics have to deal with huge amount of data efficiently. In many applications, the data are supposed to have explicit or implicit structures. To develop efficient algorithms for such data, we have to propose possible structure models and test if the models are feasible. Hence, it is important to make a compact model for structured data, and enumerate all instances efficiently. There are few graph classes besides trees that can be used for a model. In this paper, we investigate distance-hereditary graphs. This class of graphs consists of isometric graphs and hence contains trees and cographs. First, a canonical and compact tree representation of the class is proposed. The tree representation can be constructed in linear time by using prefix trees. Usually, prefix trees are used to maintain a set of strings. In our algorithm, the prefix trees are used to maintain the neighborhood of vertices, which is a new approach unlike the lexicographically breadth-first search used in other studies. Based on the canonical tree representation, efficient algorithms for the distance-hereditary graphs are proposed, including linear time algorithms for graph recognition and graph isomorphism and an efficient enumeration algorithm. An efficient coding for the tree representation is also presented; it requires [3.59n] bits for a distance-hereditary graph of n vertices and 3n bits for a cograph. The results of coding improve previously known upper bounds （both are 2^O（nlogn）） of the number of distance-hereditary graphs and cographs to 2^[3.59n] and 2^3n, respectively.

关键词： algorithmic graph theory cograph distance-hereditary graph prefix tree tree representation

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Laminar structure of ptolemaic graphs with applications

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DISCRETE APPLIED MATHEMATICS 2009年第7期157卷 1533-1543页

作者： Uehara, Ryuhei Uno, Yushi Osaka Prefecture Univ Grad Sch Sci Dept Math & Informat Sci Osaka Japan

Ptolemaic graphs are those satisfying the Ptolemaic inequality for any four vertices. The graph class coincides with the intersection of chordal graphs and distance hereditary graphs. It can also be seen as a natural generalization of block graphs (and hence trees). In this paper, we first state a laminar structure of cliques, which leads to its canonical tree representation. This result is a translation of gamma-acyclicity which appears in the context of relational database schemes. The tree representation gives a simple intersection model of ptolemaic graphs, and it is constructed in linear time from a perfect elimination ordering obtained by the lexicographic breadth first search. Hence the recognition and the graph isomorphism for ptolemaic graphs can be solved in linear time. Using the tree representation, we also give an efficient algorithm for the Hamiltonian cycle problem. (C) 2008 Elsevier B.V. All rights reserved.

关键词： algorithmic graph theory Data structures gamma-acyclicity Hamiltonian cycle Intersection model Ptolemaic graphs

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Finding good tree decompositions by local search

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Electronic Notes in Discrete Mathematics 2009年第C期32卷 43-50页

作者： van Hoesel, Stan Marchal, Bert Quantitative Economics Maastricht University Maastricht Netherlands

We present a local search algorithm, for upper bounding the tree-width of graphs. The algorithm exploits a new neighborhood structure that operates directly on a tree decomposition of the input graph, contrary to earlier work that generally used derived notions such as elimination orderings of the vertices. As a side result, we obtain an O (f (e + f))-algorithm for making tree decompositions (or triangulations) minimal in terms of fill-in. © 2009 Elsevier B.V. All rights reserved.

关键词： algorithmic graph theory local search tree decomposition tree-width

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A New Approach to graph Recognition and Applications to Distance-Hereditary graphs

A New Approach to Graph Recognition and Applications to Dist...

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4th International Conference on theory and Applications of Models of Computation

作者： Nakano, Shin-ichi Uehara, Ryuhei Uno, Takeaki Gunma Univ Fac Engn Dept Comp Sci Gunma 3768515 Japan Japan Adv Inst Sci & Technol Sch Informat Sci Ishikawa 9231292 Japan Natl Inst Informat Tokyo 1018430 Japan

ISBN: (纸本)3540725032

Algorithms used in data mining and bioinformatics have to deal with huge amount of data efficiently. In many applications, the data are supposed to have explicit or implicit structures. To develop efficient algorithms for such data, we have to propose possible structure models and test if the models are feasible. Hence, it is important to make a compact model for structured data, and enumerate all instances efficiently. There are few graph classes besides trees that can be used for a model. In this paper, we investigate distance-hereditary graphs. This class of graphs consists of isometric graphs and hence contains trees and cographs. First, a canonical and compact tree representation of the class is proposed. The tree representation can be constructed in linear time by using prefix trees. Usually, prefix trees are used to maintain a set of strings. In our algorithm, the prefix trees are used to maintain the neighborhood of vertices, which is a new approach unlike the lexicographically breadth-first search used in other studies. Based on the canonical tree representation, efficient algorithms for the distance-hereditary graphs are proposed, including linear time algorithms for graph recognition and graph isomorphism and an efficient enumeration algorithm. An efficient coding for the tree representation is also presented;it requires a OE 3.59na OE parts per thousand bits for a distance-hereditary graph of n vertices and 3n bits for a cograph. The results of coding improve previously known upper bounds (both are 2 (O(n log n))) of the number of distance-hereditary graphs and cographs to 2(a OE 3.59na OE parts per thousand) and 2(3n) , respectively.

关键词： algorithmic graph theory cograph distance-hereditary graph prefix tree tree representation

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A NEW HYBRID GENETIC ALGORITHM FOR MAXIMUM INDEPENDENT SET PROBLEM

A NEW HYBRID GENETIC ALGORITHM FOR MAXIMUM INDEPENDENT SET P...

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4th International Conference on Software and Data Technologies

作者： Mehrabi, Saeed Mehrabi, Abbas Mehrabi, Ali D. Shahid Bahonar Univ Kerman Dept Comp Sci Kerman Iran Islamic Azad Univ Dept Comp Engn South Tehran Branch Tehran Iran Yazd Univ Dept Math & Comp Sci Yazd Iran

ISBN: (纸本)9789896740108

In recent years, Genetic Algorithms (GAs) have been frequently used for many search and optimization problems. In this paper, we use genetic algorithms for solving the NP-complete maximum independent set problem (MISP). We have developed a new heuristic independent crossover (HIX) especially for MISP, introducing a new hybrid genetic algorithm (MIS-HGA). We use a repair operator to ensure that our offsprings are valid after mutation. We compare our algorithm, MIS-GA, with an efficient existing algorithm called GENEsYs. Also, a variety of benchmarks are used to test our algorithm. As the experimental results show: 1) our algorithm outperforms GENEsYs, and, 2) applying HIX to genetic algorithms with an appropriate mutation rate, gives far better performance than the classical crossover operators.

关键词： algorithmic graph theory Combinatorial Optimization Maximum Independent Set Problem Genetic Algorithms

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On computing longest paths in small graph classes

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INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE 2007年第5期18卷 911-930页

作者： Uehara, Ryuhei Uno, Yushi JAIST Sch Informat Sci Dept Informat Proc Ishikawa Japan Osaka Prefecture Univ Grad Sch Sci Dept Math & Informat Sci Sakai Osaka 5998531 Japan

The longest path problem is the one that finds a longest path in a given graph. While the graph classes in which the Hamiltonian path problem can be solved efficiently are widely investigated, few graph classes are known to be solved efficiently for the longest path problem. Among those, for trees, a simple linear time algorithm for the longest path problem is known. We first generalize the algorithm, and show that the longest path problem can be solved efficiently for some tree-like graph classes by this approach. We next propose two new graph classes that have natural interval representations, and show that the longest path problem can be solved efficiently on these classes.

关键词： algorithmic graph theory design and analysis of algorithms graph classes longest path problem

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Space efficient algorithms for directed series-parallel graphs

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JOURNAL OF ALGORITHMS 2006年第2期60卷 85-114页

作者： Jakoby, Andreas Liskiewicz, Maciej Reischuk, Ruediger Med Univ Lubeck Inst Theoret Informat D-23538 Lubeck Germany

The subclass of directed series-parallel graphs plays an important role in computer science. Whether a given graph is series-parallel is a well studied problem in algorithmic graph theory, for which fast sequential and parallel algorithms have been developed in a sequence of papers. Also methods are known to solve the reachability and the decomposition problem for series-parallel graphs time efficiently. However, no dedicated results have been obtained for the space complexity of these problems when restricted to series-parallel graphs - the topic of this paper. Deterministic algorithms are presented for the recognition, reachability, decomposition and the path counting problem for series-parallel graphs that use only logarithmic space. Since for arbitrary directed graphs reachability and path counting are believed not to be solvable in Logspace, the main contribution of this work are novel deterministic path finding routines that work correctly in series-parallel graphs, and a characterization of series-parallel graphs by forbidden subgraphs that can be tested space-efficiently. The space bounds are best possible, i.e. the decision problem is shown to be L-complete with respect to AC(0)-reductions. They have also implications for the parallel time complexity of these problems when restricted to series-parallel graphs. Finally, we sketch how these results can be generalized to extension of the series-parallel graph family: to graphs with multiple sources or multiple sinks and to the class of minimal vertex series-parallel graphs. (c) 2004 Elsevier Inc. All rights reserved.

关键词： efficient algorithms algorithmic graph theory computational complexity

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Laminar structure of ptolemaic graphs and its applications

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16th International Symposium on Algorithms and Computations (ISAAC 2005)

作者： Uehara, R Uno, Y JAIST Sch Informat Sci Tatsunokuchi Ishikawa Japan Osaka Prefecture Univ Grad Sch Sci Dept Math & Informat Sci Sakai Osaka 591 Japan

ISBN: (纸本)3540309357

Ptolemaic graphs are graphs that satisfy the Ptolemaic inequality for any four vertices. The graph class coincides with the intersection of chordal graphs and distance hereditary graphs, and it is a natural generalization of block graphs (and hence trees). In this paper, a new characterization of ptolemaic graphs is presented. It is a laminar structure of cliques, and leads us to a canonical tree representation, which gives a simple intersection model for ptolemaic graphs. The tree representation is constructed in linear time from a perfect elimination ordering obtained by the lexicographic breadth first search. Hence the recognition and the graph isomorphism for ptolemaic graphs can be solved in linear time. Using the tree representation, we also give an O(n) time algorithm for the Hamiltonian cycle problem.

关键词： algorithmic graph theory data structure Hamiltonian cycle intersection model ptolemaic graphs

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Consensus algorithms for the generation of all maximal bicliques

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DISCRETE APPLIED MATHEMATICS 2004年第1期145卷 11-21页

作者： Alexe, G Alexe, S Crama, Y Foldes, S Hammer, PL Simeone, B Rutgers State Univ RUTCOR Piscataway NJ 08854 USA Univ Liege Ecole Adm Affaires B-4000 Liege Belgium Tampere Univ Technol Dept Math FIN-33101 Tampere Finland Univ Roma La Sapienza Dept Stat I-00185 Rome Italy

We describe a new algorithm for generating all maximal bicliques (i.e. complete bipartite. not necessarily induced subgraphs) of a graph. The algorithm is inspired by, and is quite similar to. the consensus method used in propositional logic. We show that some variants of the algorithm are totally polynomial, and even incrementally polynomial. The total complexity of the most efficient variant of the algorithms presented here is polynomial in the input size. and only linear in the output size. Computational experiments demonstrate its high efficiency on randomly generated graphs with up to 2000 vertices and 20,000 edges. (C) 2003 Elsevier B.V. All rights reserved.

关键词： maximal complete bipartite subgraph biclique consensus-type algorithm algorithmic graph theory incremental polynomial enumeration

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