A fast algorithm for the maximum clique problem
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A branch-and-bound algorithm for the maximum clique problem--which is computationally equivalent to the maximum independent (stable) set problem--is presented with the vertex order taken from a coloring of the vertices and with a new pruning strategy.About:
This article is published in Discrete Applied Mathematics.The article was published on 2002-08-15 and is currently open access. It has received 645 citations till now. The article focuses on the topics: Independent set & Chordal graph.read more
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Journal ArticleDOI
Combinatorial algorithms for the maximum k-plex problem
Benjamin McClosky,Illya V. Hicks +1 more
TL;DR: A new upper bound on the cardinality of k-plexes is derived and combinatorial clique algorithms to find maximum k-Plexes are adapted.
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Clique Relaxation Models in Social Network Analysis
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On inclusionwise maximal and maximum cardinality k-clubs in graphs
TL;DR: This article settles an open problem establishing the intractability of testing inclusion-wise maximality of k -clubs, and proposes a distance coloring based upper-bounding scheme and a bounded enumeration based lower- bounding routine and employ them in a combinatorial branch-and-bound algorithm for finding maximum cardinality k - clubs.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book ChapterDOI
The maximum clique problem
TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.
Journal ArticleDOI
An exact algorithm for the maximum clique problem
TL;DR: In this paper, a partially enumerative algorithm for the maximum clique problem is presented, which is very simple to implement on an IBM 3090 computer and can be used to generate graphs with up to 3000 vertices and over one million edges.