Fast Algorithms for the Maximum Clique Problem on Massive Sparse Graphs

  • Bharath Pattabiraman
  • Md. Mostofa Ali Patwary
  • Assefaw H. Gebremedhin
  • Wei-keng Liao
  • Alok Choudhary
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8305)


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 quickly find maximum cliques in large sparse graphs. 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.


Exact Algorithm Maximum Clique Community Detection Sparse Graph Optimal Power Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Bharath Pattabiraman
    • 1
  • Md. Mostofa Ali Patwary
    • 1
  • Assefaw H. Gebremedhin
    • 2
  • Wei-keng Liao
    • 1
  • Alok Choudhary
    • 1
  1. 1.Northwestern UniversityEvanstonUSA
  2. 2.Purdue UniversityWest LafayetteUSA

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