Solving the Maximum Clique Problem on a Class of Network Graphs, With Application to Social Networks
01 Jun 2008-
TL;DR: This work forms the maximum clique problem on undirected graphs and develops two algorithms to solve it: a pruning algorithm and an enumeration algorithm that successively improves an upper bound on the clique number of a graph and finds larger and larger cliques in the graph.
Abstract: : Social network analysis frequently uses the idea of a clique in a network to identify key subgroups of highly-connected members of the network. We formulate the maximum clique problem on undirected graphs and develop two algorithms to solve it: a pruning algorithm and an enumeration algorithm. The pruning algorithm successively improves an upper bound on the clique number of a graph, and the enumeration algorithm successively finds larger and larger cliques in the graph. Both terminate with a maximum clique in the graph, and, when run together, provide an interval of uncertainty on the size of a maximum clique in a graph that converges to zero. We apply our algorithms to real examples in the modeling of terrorist social networks, and determine that our algorithms are efficient and practical for problems of moderate size.
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17 Aug 2017
TL;DR: This paper proposes an improved version of the k – opt Local Search (KLS), which is a variable depth search based algorithm suggested by Kengo Katayama, Akihiro Hamamoto and Hiroyuki Narihisa for the maximum clique problem.
Abstract: The Maximum Clique Problem (MCP) is a combinatorial optimization problem which has important practical applications like social networking, computer vision, pattern recognition,... The MCP is known to be NP-hard and recently has received much attention from the scientific community. In this paper we propose an improved version of the k – opt Local Search (KLS), which is a variable depth search based algorithm suggested by Kengo Katayama, Akihiro Hamamoto and Hiroyuki Narihisa for the maximum clique problem. Extensive testing on 34 DIMACS benchmark graphs shows good results in comparison to the original KLS.
Cites background from "Solving the Maximum Clique Problem ..."
...Bài toán MCP có những ứng dụng quan trọng trong lĩnh vực khoa học, kĩ thuật; chẳng hạn như: Mạng xã hội [12] , tạo lịch trình thực hiện các tiến trình trên máy tính (Scheduling) [2], đánh nhãn bản đồ (Map Labeling) [13], thị giác máy tính (Computer Vision) [5],....
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...[12] Spyridon Pollatos, “Solving the maximum clique problem on a class of network graphs, with application to social networks”, Naval postgraduate school, pp....
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01 Jan 1979
42,654 citations
Book•
01 Jan 1979
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.
Abstract: This is the second edition of a quarterly column the purpose of which is to provide 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 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed. Readers having results they would like mentioned (NP-hardness, PSPACE-hardness, polynomial-time-solvability, etc.), or open problems they would like publicized, should send them to David S. Johnson, Room 2C355, Bell Laboratories, Murray Hill, NJ 07974, including details, or at least sketches, of any new proofs (full papers are preferred). In the case of unpublished results, please state explicitly that you would like the results mentioned in the column. Comments and corrections are also welcome. For more details on the nature of the column and the form of desired submissions, see the December 1981 issue of this journal.
40,020 citations
01 Jan 1979
12,336 citations
Book•
30 Dec 1991
TL;DR: In this article, the development of social network analysis, tracing its origins in classical sociology and its more recent formulation in social scientific and mathematical work, is described and discussed. But it is argued that the analysis of social networks is not a purely static process.
Abstract: This paper reports on the development of social network analysis, tracing its origins in classical sociology and its more recent formulation in social scientific and mathematical work. It is argued...
6,366 citations
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].
1,065 citations