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

2008
*
Communications in Computer and Information Science
*

In this paper

doi:10.1007/978-3-540-87477-5_18
fatcat:e46p5masingxnf7hpclw6o44pm
*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*. ...##
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Multi-neighborhood tabu search for the maximum weight clique problem

2012
*
Annals of Operations Research
*

Computational results disclose that our

doi:10.1007/s10479-012-1124-3
fatcat:5nj3xzvdzja2lawaysagno6rpi
*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*...##
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The Maximum Clique Problem
[chapter]

1999
*
Handbook of Combinatorial Optimization
*

In this paper we present

doi:10.1007/978-1-4757-3023-4_1
fatcat:5s6fqfs52rafteadmhral2kgpy
*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*. ...##
###
The maximum clique problem

1994
*
Journal of Global Optimization
*

In this paper we present

doi:10.1007/bf01098364
fatcat:qmknkbopunaijoi7joaaab3rey
*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*. ...##
###
Approximation Algorithms for Some Graph Partitioning Problems
[chapter]

2004
*
Graph Algorithms and Applications 2
*

Equivalently, given

doi:10.1142/9789812794741_0002
fatcat:rpu63vp3ird4flehii7moblcou
*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. ...##
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Approximation Algorithms for Some Graph Partitioning Problems

2000
*
Journal of Graph Algorithms and Applications
*

Equivalently, given

doi:10.7155/jgaa.00021
fatcat:3rrl52falnfwnhv3rdvfivl4tu
*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. ...##
###
Some approximation algorithms for the clique partition problem in weighted interval graphs

2007
*
Theoretical Computer Science
*

In this paper, we study

doi:10.1016/j.tcs.2007.04.030
fatcat:tswbtmmzsna4jdrq5ve7hdg5xq
*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 ...##
###
On Maximum Weight Clique Algorithms, and How They Are Evaluated
[chapter]

2017
*
Lecture Notes in Computer Science
*

We look at other families of benchmark instances

doi:10.1007/978-3-319-66158-2_14
fatcat:4zde5prxineghctbygnonghrve
*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. ...##
###
An Exact Parallel Algorithm for the Maximum Clique Problem
[chapter]

1998
*
Applied Optimization
*

In this paper we present

doi:10.1007/978-1-4613-3279-4_18
fatcat:gspmbzhmgjfjvmmo7r6wrc7c6u
*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*. ...##
###
Solving Maximum Clique Problem for Protein Structure Similarity
[article]

2009
*
arXiv
*
pre-print

In addition, we designed

arXiv:0901.4833v1
fatcat:ruva6tcynna47kjkeomf5j5cvy
*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*. ...##
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Approximating the maximum weight clique using replicator dynamics

2000
*
IEEE Transactions on Neural Networks
*

Given an undirected graph with

doi:10.1109/72.883403
pmid:18249849
fatcat:jkq7iuag2nav7c5zexfavjeit4
*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*. ...##
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Trapezoid graphs and generalizations, geometry and algorithms

1997
*
Discrete Applied Mathematics
*

Based on

doi:10.1016/s0166-218x(96)00013-3
fatcat:trxcwgwz6bddtir4m3xchfeega
*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. ...##
###
Trapezoid graphs and generalizations, geometry and algorithms
[chapter]

1994
*
Lecture Notes in Computer Science
*

Based on

doi:10.1007/3-540-58218-5_13
fatcat:rh53ocuvvfgzjluvpsy4b7ugze
*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. ...##
###
New lower bounds on the weighted chromatic number of a graph

2004
*
Discussiones Mathematicae Graph Theory
*

In particular, we study different ways of

doi:10.7151/dmgt.1224
fatcat:aaezufu6pfgtxgip4hbevljvey
*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*. ...##
###
A scalable algorithm for the market basket analysis

2007
*
Journal of Retailing and Consumer Services
*

In this approach,

doi:10.1016/j.jretconser.2007.02.003
fatcat:bs3fbzmumjaqnnwfef6h5tob7i
*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 ...
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