scispace - formally typeset
Topic

Clique problem

About: Clique problem is a(n) research topic. Over the lifetime, 1252 publication(s) have been published within this topic receiving 31280 citation(s).
Papers
More filters

Book ChapterDOI
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.
Abstract: The maximum clique problem is a classical problem in combinatorial optimization which finds important applications in different domains. In this paper we try to give a survey of results concerning algorithms, complexity, and applications of this problem, and also provide an updated bibliography. Of course, we build upon precursory works with similar goals [39, 232, 266].

1,041 citations


Journal ArticleDOI
TL;DR: Clique width is bound in terms of its tree width on the one hand, and of the clique width of its edge complement on the other, to reduce the complexity measure of graphs associated with hierarchical decompositions.
Abstract: Hierarchical decompositions of graphs are interesting for algorithmic purposes. Many NP complete problems have linear complexity on graphs with tree-decompositions of bounded width. We investigate alternate hierarchical decompositions that apply to wider classes of graphs and still enjoy good algorithmic properties. These decompositions are motivated and inspired by the study of vertex-replacement context-free graph grammars. The complexity measure of graphs associated with these decompositions is called clique width . In this paper we bound the clique width of a graph in terms of its tree width on the one hand, and of the clique width of its edge complement on the other.

653 citations


Journal ArticleDOI
TL;DR: 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.
Abstract: Given a graph, in the maximum clique problem, one desires to find the largest number of vertices, any two of which are adjacent. 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. The algorithm performs successfully for many instances when applied to random graphs and DIMACS benchmark graphs.

609 citations


Journal ArticleDOI
17 Oct 1997-Science
TL;DR: The maximal clique problem has been solved by means of molecular biology techniques and the algorithm is highly parallel and has satisfactory fidelity, representing further evidence for the ability of DNA computing to solve NP-complete search problems.
Abstract: The maximal clique problem has been solved by means of molecular biology techniques. A pool of DNA molecules corresponding to the total ensemble of six-vertex cliques was built, followed by a series of selection processes. The algorithm is highly parallel and has satisfactory fidelity. This work represents further evidence for the ability of DNA computing to solve NP-complete search problems.

596 citations


Book ChapterDOI
01 Jan 1993-
Abstract: Clique trees and chordal graphs have carved out a niche for themselves in recent work on sparse matrix algorithms, due primarily to research questions associated with advanced computer architectures. This paper is a unified and elementary introduction to the standard characterizations of chordal graphs and clique trees. The pace is leisurely, as detailed proofs of all results are included. We also briefly discuss applications of chordal graphs and clique trees in sparse matrix computations.

475 citations


Network Information
Related Topics (5)
Time complexity

36K papers, 879.5K citations

91% related
Approximation algorithm

23.9K papers, 654.3K citations

89% related
Clique (graph theory)

1.2K papers, 28.1K citations

88% related
Edge cover

1.5K papers, 35.3K citations

88% related
Vertex cover

3.4K papers, 91.4K citations

88% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20223
202136
202048
201945
201854
201762

Top Attributes

Show by:

Topic's top 5 most impactful authors

Panos M. Pardalos

19 papers, 2.6K citations

Marcello Pelillo

19 papers, 1.8K citations

Patrick Prosser

13 papers, 284 citations

Sameh Sorour

11 papers, 269 citations

Mohamed-Slim Alouini

7 papers, 231 citations