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On Importance of a Special Sorting in the Maximum-Weight Clique Algorithm Based on Colour Classes [chapter]

Deniss Kumlander
2008 Communications in Computer and Information Science  
In this paper a new sorting strategy is proposed to be used in the maximum weight clique finding algorithm, which is known to be the fastest at the moment.  ...  That is why the right ordering before colouring is so crucial before executing the heuristic colouring and consequently the main maximum weight clique searching routine.  ...  The maximum-weight clique problem asks for a clique of the maximum weight. The weighted clique number is the total weight of weighted maximum clique.  ... 
doi:10.1007/978-3-540-87477-5_18 fatcat:e46p5masingxnf7hpclw6o44pm

Multi-neighborhood tabu search for the maximum weight clique problem

Qinghua Wu, Jin-Kao Hao, Fred Glover
2012 Annals of Operations Research  
Computational results disclose that our new tabu search algorithm outperforms the leading algorithm for the maximum weight clique problem, and in addition rivals the performance of the best methods for  ...  Let w:V→Z + be a weighting function that assigns to each vertex i∈V a positive integer. The maximum weight clique problem (MWCP) is to determine a clique of maximum weight.  ...  Computational results disclose that our new tabu search algorithm outperforms the leading algorithm for the maximum weight clique problem, and in addition rivals the performance of the best methods for  ... 
doi:10.1007/s10479-012-1124-3 fatcat:5nj3xzvdzja2lawaysagno6rpi

The Maximum Clique Problem [chapter]

Immanuel M. Bomze, Marco Budinich, Panos M. Pardalos, Marcello Pelillo
1999 Handbook of Combinatorial Optimization  
In this paper we present a survey of results concerning algorithms, complexity, and applications of the maximum clique problem.  ...  We discuss enumerative and exact algorithms, heuristics, and a variety of other proposed methods. An up to date bibliography on the maximum clique and related problems is also provided.  ...  A clique C is a subset of V such that G(C) is complete. The maximum clique problem asks for a clique of maximum weight.  ... 
doi:10.1007/978-1-4757-3023-4_1 fatcat:5s6fqfs52rafteadmhral2kgpy

The maximum clique problem

Panos M. Pardalos, Jue Xue
1994 Journal of Global Optimization  
In this paper we present a survey of results concerning algorithms, complexity, and applications of the maximum clique problem.  ...  We discuss enumerative and exact algorithms, heuristics, and a variety of other proposed methods. An up to date bibliography on the maximum clique and related problems is also provided.  ...  A clique C is a subset of V such that G(C) is complete. The maximum clique problem asks for a clique of maximum weight.  ... 
doi:10.1007/bf01098364 fatcat:qmknkbopunaijoi7joaaab3rey

Approximation Algorithms for Some Graph Partitioning Problems [chapter]

G. He, J. Liu, C. Zhao
2004 Graph Algorithms and Applications 2  
Equivalently, given a weighted complete k-partite graph, cover its vertices with a minimum number of disjoint cliques in such a way that the total weight of the cliques is maximized or minimized.  ...  This paper considers problems of the following type: given an edgeweighted k-colored input graph with maximum color class size c, find a minimum or maximum c-way cut such that each color class is totally  ...  Acknowledgments We thank the anonymous referees for their valuable comments.  ... 
doi:10.1142/9789812794741_0002 fatcat:rpu63vp3ird4flehii7moblcou

Approximation Algorithms for Some Graph Partitioning Problems

G. He, J. Liu, C. Zhao
2000 Journal of Graph Algorithms and Applications  
Equivalently, given a weighted complete k-partite graph, cover its vertices with a minimum number of disjoint cliques in such a way that the total weight of the cliques is maximized or minimized.  ...  This paper considers problems of the following type: given an edgeweighted k-colored input graph with maximum color class size c, find a minimum or maximum c-way cut such that each color class is totally  ...  Acknowledgments We thank the anonymous referees for their valuable comments.  ... 
doi:10.7155/jgaa.00021 fatcat:3rrl52falnfwnhv3rdvfivl4tu

Some approximation algorithms for the clique partition problem in weighted interval graphs

Mingxia Chen, Jianbo Li, Jianping Li, Weidong Li, Lusheng Wang
2007 Theoretical Computer Science  
In this paper, we study a new combinatorial optimization problem, named the minimum clique partition problem with constrained bounds, in weighted interval graphs.  ...  algorithms with different constant factors for this problem; (3) for the version where all intervals have the same weights, we design an optimal algorithm to solve the problem in linear time.  ...  Acknowledgements The authors are very grateful to two anonymous referees whose helpful suggestions and comments have led to a substantially improved presentation of the paper. Mingxia  ... 
doi:10.1016/j.tcs.2007.04.030 fatcat:tswbtmmzsna4jdrq5ve7hdg5xq

On Maximum Weight Clique Algorithms, and How They Are Evaluated [chapter]

Ciaran McCreesh, Patrick Prosser, Kyle Simpson, James Trimble
2017 Lecture Notes in Computer Science  
We look at other families of benchmark instances for the maximum weight clique problem, coming from winner determination problems, graph colouring, and error-correcting codes, and introduce two new families  ...  Maximum weight clique and maximum weight independent set solvers are often benchmarked using maximum clique problem instances, with weights allocated to vertices by taking the vertex number mod 200 plus  ...  Acknowledgements The REF instance generator was joint work with David Manlove. We are grateful to David for this, and for helpful discussions on kidney exchange.  ... 
doi:10.1007/978-3-319-66158-2_14 fatcat:4zde5prxineghctbygnonghrve

An Exact Parallel Algorithm for the Maximum Clique Problem [chapter]

Panos M. Pardalos, Jonas Rappe, Mauricio G. C. Resende
1998 Applied Optimization  
In this paper we present a portable exact parallel algorithm for the maximum clique problem on general graphs.  ...  The algorithm is based on the Carraghan-Pardalos exact algorithm (for unweighted graphs) and incorporates a variant of the greedy randomized adaptive search procedure (GRASP) for maximum independent set  ...  A similar nonlinear programming formulation has been recently obtained for the weighted maximum clique problem [17] . The weighted maximum clique problem asks for the clique of maximum weight.  ... 
doi:10.1007/978-1-4613-3279-4_18 fatcat:gspmbzhmgjfjvmmo7r6wrc7c6u

Solving Maximum Clique Problem for Protein Structure Similarity [article]

Noël Malod-Dognin , Nicola Yanev
2009 arXiv   pre-print
In addition, we designed a dedicated branch and bound algorithm for solving the maximum cardinality clique problem.  ...  In this paper we present a new integer programming formulation for solving such clique problems. The model has been implemented using the ILOG CPLEX Callable Library.  ...  The Maximum Edge Weighted clique problem MEW consists in finding a clique with a maximum sum of edge weights.  ... 
arXiv:0901.4833v1 fatcat:ruva6tcynna47kjkeomf5j5cvy

Approximating the maximum weight clique using replicator dynamics

V. Stix, M. Pelillo, I.R. Bomze
2000 IEEE Transactions on Neural Networks  
Given an undirected graph with weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having the largest total weight.  ...  Although there has recently been much interest around neural-network algorithms for the unweighted maximum clique problem, no effort has been directed so far toward its weighted counterpart.  ...  ACKNOWLEDGMENT The authors would like to thank L. Babel for kind support, especially for providing us with the original code of his algorithm.  ... 
doi:10.1109/72.883403 pmid:18249849 fatcat:jkq7iuag2nav7c5zexfavjeit4

Trapezoid graphs and generalizations, geometry and algorithms

Stefan Felsner, Rudolf Müller, Lorenz Wernisch
1997 Discrete Applied Mathematics  
Based on a geometric representation of trapezoid graphs by boxes in the plane we design optimal, i.e., O(n log n), algorithms for chromatic number, weighted independent set, clique cover and maximum weighted  ...  They propose an O(n 2 ) algorithm for chromatic number and a less e cient algorithm for maximum clique on trapezoid graphs.  ...  Let us review the main steps of the a polynomial algorithm for the maximum clique problem of CT-graphs. First, the algorithm searches for a maximum Hellyclique in G.  ... 
doi:10.1016/s0166-218x(96)00013-3 fatcat:trxcwgwz6bddtir4m3xchfeega

Trapezoid graphs and generalizations, geometry and algorithms [chapter]

Stefan Felsner, Rudolf Müller, Lorenz Wernisch
1994 Lecture Notes in Computer Science  
Based on a geometric representation of trapezoid graphs by boxes in the plane we design optimal, i.e., O(n log n), algorithms for chromatic number, weighted independent set, clique cover and maximum weighted  ...  They propose an O(n 2 ) algorithm for chromatic number and a less e cient algorithm for maximum clique on trapezoid graphs.  ...  Let us review the main steps of the a polynomial algorithm for the maximum clique problem of CT-graphs. First, the algorithm searches for a maximum Hellyclique in G.  ... 
doi:10.1007/3-540-58218-5_13 fatcat:rh53ocuvvfgzjluvpsy4b7ugze

New lower bounds on the weighted chromatic number of a graph

Massimiliano Caramia, Jirí Fiala
2004 Discussiones Mathematicae Graph Theory  
In particular, we study different ways of a possible improvement of the lower bound offered by a maximum weighted clique.  ...  In this paper we present theoretical and algorithmic results for the computation of lower bounds on the chromatic number of a weighted graph.  ...  Observe also, that for a perfect graph G, the weighted chromatic number of G, is equal to the weight of a maximum weighted clique.  ... 
doi:10.7151/dmgt.1224 fatcat:aaezufu6pfgtxgip4hbevljvey

A scalable algorithm for the market basket analysis

Luís Cavique
2007 Journal of Retailing and Consumer Services  
In this approach, the condensed data is used and is obtained by transforming the market basket problem into a maximum-weighted clique problem.  ...  Firstly, the input dataset is transformed into a graph-based structure and then the maximum-weighted clique problem is solved using a meta-heuristic approach in order to find the most frequent itemsets  ...  In section 3 we present the Similis algorithm, which first of all transforms the input dataset into a graph-based structure, and then the new problem, the weighted clique problem, is solved using a meta-heuristic  ... 
doi:10.1016/j.jretconser.2007.02.003 fatcat:bs3fbzmumjaqnnwfef6h5tob7i
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