A fast algorithm for the maximum clique problem
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TLDR
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
Citations
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Proceedings Article
Applying AI and incomplete solution principles to solve NP-hard problems in the real-time systems
TL;DR: Experiments conducted in this paper have demonstrated that the meta-algorithm in a randomly generated graphs environment required up to 3 times less time to find a solution in a certain range of graphs than the best known general type algorithm, and was never slower in other ranges.
Solving the maximum clique problem using intelligent water drops algorithm
TL;DR: In the new IWDs algorithm, the water drop possesses SOLVING the maximum clique problem, which allows water drop to carry an amount of soil while it is moving from one place to another.
Journal ArticleDOI
On comparing algorithms for the maximum clique problem
TL;DR: It is shown that a broad class of branch and bound algorithms for the maximum clique problem display sub-exponential average running time behavior, and it is shown how this helps to explain the apparent discrepancy between the theoretical and experimental results.
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.