A review on algorithms for maximum clique problems

•We provide an updated review of exact and heuristic algorithms for maximum clique problems.•We classify the search strategies and put forward the key ingredients of the reviewed methods.•This is aimed to encourage more research on new solution algorithms.•This is aimed to motivate more applications...

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Bibliographic Details
Published in:European journal of operational research Vol. 242; no. 3; pp. 693 - 709
Main Authors: Wu, Qinghua, Hao, Jin-Kao
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.05.2015
Elsevier Sequoia S.A
Elsevier
Subjects:
Algorithms
Applications
Classification
Combinatorial analysis
Combinatorics
Computer Science
Exact algorithms
Graph algorithms
Graphs
Heuristic
Heuristics
Ingredients
Mathematical problems
Maximum clique problems
Operational research
Searching
Strategy
Studies
Applications
Heuristics
Maximum clique problems
Exact algorithms
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•We provide an updated review of exact and heuristic algorithms for maximum clique problems.•We classify the search strategies and put forward the key ingredients of the reviewed methods.•This is aimed to encourage more research on new solution algorithms.•This is aimed to motivate more applications of using clique approaches. The maximum clique problem (MCP) is to determine in a graph a clique (i.e., a complete subgraph) of maximum cardinality. The MCP is notable for its capability of modeling other combinatorial problems and real-world applications. As one of the most studied NP-hard problems, many algorithms are available in the literature and new methods are continually being proposed. Given that the two existing surveys on the MCP date back to 1994 and 1999 respectively, one primary goal of this paper is to provide an updated and comprehensive review on both exact and heuristic MCP algorithms, with a special focus on recent developments. To be informative, we identify the general framework followed by these algorithms and pinpoint the key ingredients that make them successful. By classifying the main search strategies and putting forward the critical elements of the most relevant clique methods, this review intends to encourage future development of more powerful methods and motivate new applications of the clique approaches.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2014.09.064