Fast algorithms for the maximum clique problem on massive graphs with applications to overlapping community detection

Bharath Pattabiraman*, Md Mostofa Ali Patwary, Assefaw H. Gebremedhin, Wei Keng Liao, Alok Choudhary

*Corresponding author for this work

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

The maximum clique problem is a well-known NP-hard problem with applications in data mining, network analysis, information retrieval, and many other areas related to the World Wide Web. There exist several algorithms for the problem, with acceptable runtimes for certain classes of graphs, but many of them are infeasible for massive graphs.We present a new exact algorithm that employs novel pruning techniques and is able to find maximum cliques in very large, sparse graphs quickly. Extensive experiments on different kinds of synthetic and real-world graphs show that our new algorithm can be orders of magnitude faster than existing algorithms. We also present a heuristic that runs orders of magnitude faster than the exact algorithm while providing optimal or near-optimal solutions.We illustrate a simple application of the algorithms in developing methods for detection of overlapping communities in networks.

Original languageEnglish (US)
Pages (from-to)421-448
Number of pages28
JournalInternet Mathematics
Volume11
Issue number4
DOIs
StatePublished - Jan 1 2015

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics

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