Abstract
The maximal biclique enumeration (MBE) is a problem of identifying all maximal bicliques in a bipartite graph. Once enumerated in a bipartite graph, maximal bicliques can be used to solve problems in areas such as purchase prediction, statistic analysis of social networks, discovery of interesting structures in protein-protein interaction networks, identification of common gene-set associations, and integration of diverse functional genomes data. In this paper, we develop an optimized sequential MBE algorithm called \(\mathsf {sMBEA}\) for sparse bipartite graphs which appear frequently in real life. The results of extensive experiments on several real-life data sets demonstrate that \(\mathsf {sMBEA}\) outperforms the state-of-the-art sequential algorithm \(\mathsf {iMBEA}\).
Keywords
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Agarwal, P.K., Alon, N., Aronov, B., Suri, S.: Can visibility graphs be represented compactly? Discrete Comput. Geom. 12(3), 347–365 (1994)
Alexe, G., Alexe, S., Crama, Y., Foldes, S., Hammer, P.L., Simeone, B.: Consensus algorithms for the generation of all maximal bicliques. Discrete Appl. Math. 145(1), 11–21 (2004)
Bron, C., Kerbosch, J.: Algorithm 457: finding all cliques of an undirected graph. Commun. ACM 16(9), 575–577 (1973)
Brown, R.G.: Maximizing beowulf performance. In: Annual Linux Showcase & Conference (2000)
Cheng, Y., Church, G.: Biclustering of expression data. In: 2000 Proceedings of Intelligent Systems for Molecular Biology (2000)
Chesler, E.J., Wang, J., Lu, L., Qu, Y., Manly, K.F., Williams, R.W.: Genetic correlates of gene expression in recombinant inbred strains. Neuroinformatics 1(4), 343–357 (2003)
Colantonio, A., Di Pietro, R., Ocello, A., Verde, N.V.: Taming role mining complexity in RBAC. Comput. Secur. 29(5), 548–564 (2010)
Eppstein, D.: Arboricity and bipartite subgraph listing algorithms. Inf. Process. Lett. 51(4), 207–211 (1994)
Jermaine, C.: Finding the most interesting correlations in a database: how hard can it be? Inf. Syst. 30(1), 21–46 (2005)
Johnson, D.S., Yannakakis, M., Papadimitriou, C.H.: On generating all maximal independent sets. Inf. Process. Lett. 27(3), 119–123 (1988)
Kaytoue-Uberall, M., Duplessis, S., Napoli, A.: Using formal concept analysis for the extraction of groups of co-expressed genes. In: Le Thi, H.A., Bouvry, P., Pham Dinh, T. (eds.) MCO 2008. CCIS, vol. 14, pp. 439–449. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-87477-5_47
Kreek, M.J., Nielsen, D.A., LaForge, K.S.: Genes associated with addiction. NeuroMol. Med. 5(1), 85–108 (2004)
Li, J., Li, H., Soh, D., Wong, L.: A correspondence between maximal complete bipartite subgraphs and closed patterns. In: Jorge, A.M., Torgo, L., Brazdil, P., Camacho, R., Gama, J. (eds.) PKDD 2005. LNCS (LNAI), vol. 3721, pp. 146–156. Springer, Heidelberg (2005). https://doi.org/10.1007/11564126_18
Li, J., Liu, G., Li, H., Wong, L.: Maximal biclique subgraphs and closed pattern pairs of the adjacency matrix: a one-to-one correspondence and mining algorithms. IEEE Trans. Knowl. Data Eng. 19(12), 1625–1637 (2007)
Liu, G., Sim, K., Li, J.: Efficient mining of large maximal bicliques. In: Tjoa, A.M., Trujillo, J. (eds.) DaWaK 2006. LNCS, vol. 4081, pp. 437–448. Springer, Heidelberg (2006). https://doi.org/10.1007/11823728_42
Makino, K., Uno, T.: New algorithms for enumerating all maximal cliques. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 260–272. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27810-8_23
Malgrange, Y.: Recherche des sous-matrices premières d’unematrice à coefficients binaires. applications à certainsproblèmes de graphe. In: Proceedings of the DeuxièmeCongrès de l’AFCALTI, pp. 231–242 (1962)
Mash, D.C., Adi, N., Qin, Y., Buck, A., Pablo, J., et al.: Gene expression in human hippocampus from cocaine abusers identifies genes which regulate extracellular matrix remodeling. PLoS One 2(11), e1187 (2007)
Mouret, S., Grossmann, I.E., Pestiaux, P.: Time representations and mathematical models for process scheduling problems. Comput. Chem. Eng. 35(6), 1038–1063 (2011)
Mukherjee, A.P., Tirthapura, S.: Enumerating maximal bicliques from a large graph using mapreduce. IEEE Trans. Serv. Comput. 10(5), 771–784 (2017)
Mushlin, R.A., Kershenbaum, A., Gallagher, S.T., Rebbeck, T.R.: A graph-theoretical approach for pattern discovery in epidemiological research. IBM Syst. J. 46(1), 135–149 (2007)
Peeters, R.: The maximum edge biclique problem is NP-complete. Discrete Appl. Math. 131(3), 651–654 (2003)
Sanderson, M.J., Driskell, A.C., Ree, R.H., Eulenstein, O., Langley, S.: Obtaining maximal concatenated phylogenetic data sets from large sequence databases. Mol. Biol. Evol. 20(7), 1036–1042 (2003)
Tanay, A., Sharan, R., Shamir, R.: Discovering statistically significant biclusters in gene expression data. Bioinformatics 18(Supp. 1), S136–S144 (2002)
Tomita, E., Tanaka, A., Takahashi, H.: The worst-case time complexity for generating all maximal cliques and computational experiments. Theor. Comput. Sci. 363(1), 28–42 (2006)
Yoshinaka, R.: Towards dual approaches for learning context-free grammars based on syntactic concept lattices. In: Mauri, G., Leporati, A. (eds.) DLT 2011. LNCS, vol. 6795, pp. 429–440. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22321-1_37
Zaki, M.J., Hsiao, C.J.: Charm: an efficient algorithm for closed itemset mining. In: Proceedings of the 2002 SIAM International Conference on Data Mining, pp. 457–473. SIAM (2002)
Zaki, M.J., Ogihara, M.: Theoretical foundations of association rules. In: 3rd ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery, pp. 71–78 (1998)
Zhang, Y., Chesler, E.J., Langston, M.A.: On finding bicliques in bipartite graphs: a novel algorithm with application to the integration of diverse biological data types, p. 473. IEEE (2008)
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He, Y., Li, R., Mao, R. (2018). An Optimized MBE Algorithm on Sparse Bipartite Graphs. In: Qiu, M. (eds) Smart Computing and Communication. SmartCom 2018. Lecture Notes in Computer Science(), vol 11344. Springer, Cham. https://doi.org/10.1007/978-3-030-05755-8_21
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