A Parallel Algorithm for Enumerating All Maximal Cliques in Complex Network

Efficient enumeration of all maximal cliques in a given graph has many applications in graph theory, data mining and bio informatics. However, the exponentially increasing computation time of this problem confines the scale of the graph. Meanwhile, recent researches show that many networks in our world are complex networks involving massive data. To solve the maximal clique problem in the real-world scenarios, this paper presents a parallel algorithm Peamc (parallel enumeration of all maximal cliques) which exploits several new and effective techniques to enumerate all maximal cliques in a complex network. Furthermore, we provide a performance study on a true-life call graph with up to 2,423,807 vertices and 5,317,183 edges. The experimental results show that Peamc can find all the maximal cliques in a complex network with high efficiency and scalability

[1]  Akira Tanaka,et al.  The Worst-Case Time Complexity for Generating All Maximal Cliques , 2004, COCOON.

[2]  Mihalis Yannakakis,et al.  On Generating All Maximal Independent Sets , 1988, Inf. Process. Lett..

[3]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[4]  Jianyong Wang,et al.  Coherent closed quasi-clique discovery from large dense graph databases , 2006, KDD '06.

[5]  Akira Tanaka,et al.  The worst-case time complexity for generating all maximal cliques and computational experiments , 2006, Theor. Comput. Sci..

[6]  Hector J. Levesque,et al.  Support Set Selection for Abductive and Default Reasoning , 1996, Artif. Intell..

[7]  Christos Faloutsos,et al.  Graphs over time: densification laws, shrinking diameters and possible explanations , 2005, KDD '05.

[8]  Kazuhisa Makino,et al.  New Algorithms for Enumerating All Maximal Cliques , 2004, SWAT.

[9]  Panos M. Pardalos,et al.  The maximum clique problem , 1994, J. Glob. Optim..

[10]  Patric R. J. Östergård,et al.  A fast algorithm for the maximum clique problem , 2002, Discret. Appl. Math..

[11]  Kazuhisa Makino,et al.  On computing all abductive explanations , 2002, AAAI/IAAI.

[12]  Journal of Molecular Biology , 1959, Nature.

[13]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[14]  Shuji Tsukiyama,et al.  A New Algorithm for Generating All the Maximal Independent Sets , 1977, SIAM J. Comput..

[15]  Heikki Mannila,et al.  Fast Discovery of Association Rules , 1996, Advances in Knowledge Discovery and Data Mining.

[16]  Robert E. Tarjan,et al.  Bounds on Backtrack Algorithms for Listing Cycles, Paths, and Spanning Trees , 1975, Networks.

[17]  C. Bron,et al.  Algorithm 457: finding all cliques of an undirected graph , 1973 .

[18]  김삼묘,et al.  “Bioinformatics” 특집을 내면서 , 2000 .

[19]  Joydeep Ghosh,et al.  CLUMP: a scalable and robust framework for structure discovery , 2005, Fifth IEEE International Conference on Data Mining (ICDM'05).

[20]  BronCoen,et al.  Algorithm 457: finding all cliques of an undirected graph , 1973 .

[21]  A. Venter,et al.  Journal of The American Society for Mass Spectrometry , 2005, Journal of the American Society for Mass Spectrometry.

[22]  Etsuji Tomita,et al.  An Efficient Branch-and-Bound Algorithm for Finding a Maximum Clique , 2003, DMTCS.

[23]  Ravi Kumar,et al.  Trawling the Web for Emerging Cyber-Communities , 1999, Comput. Networks.

[24]  Thomas H. Cormen,et al.  Introduction to algorithms [2nd ed.] , 2001 .

[25]  Ramakrishnan Srikant,et al.  Fast Algorithms for Mining Association Rules in Large Databases , 1994, VLDB.

[26]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[27]  Lise Getoor,et al.  Introduction to the special issue on link mining , 2005, SKDD.

[28]  John Scott.  Social Network Analysis , 1988 .

[29]  N. Samatova,et al.  On the Relative Efficiency of Maximal Clique Enumeration Algorithms , with Application to High-Throughput Computational Biology , 2005 .

[30]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[31]  Thomas Linke,et al.  Visualizing plant metabolomic correlation networks using clique-metabolite matrices , 2001, Bioinform..