Abstract
A fundamental problem in analysing biological networks is the identification of dense subgraphs, since they are considered to be related to relevant parts of networks, like communities. Many contributions have been focused mainly in computing a single dense subgraph, but in many applications we are interested in finding a set of dense, possibly overlapping, subgraphs. In this paper we consider the Top-k-Overlapping Densest Subgraphs problem, that aims at finding a set of k dense subgraphs, for some integer \(k \ge 1\), that maximize an objective function that consists of the density of the subgraphs and the distance among them. We design a new heuristic for the Top-k-Overlapping Densest Subgraphs and we present an experimental analysis that compares our heuristic with an approximation algorithm developed for Top-k-Overlapping Densest Subgraphs (called DOS) on biological networks. The experimental result shows that our heuristic provides solutions that are denser than those computed by DOS, while the solutions computed by DOS have a greater distance. As for time-complexity, the DOS algorithm is much faster than our method.
This paper was supported by STARS Supporting Talented Research.
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References
Alba, R.D.: A graph-theoretic definition of a sociometric clique. J. Math. Sociol. 3, 113–126 (1973)
Asahiro, Y., Iwama, K., Tamaki, H., Tokuyama, T.: Greedily finding a dense subgraph. In: Karlsson, R., Lingas, A. (eds.) SWAT 1996. LNCS, vol. 1097, pp. 136–148. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61422-2_127
Balalau, O.D., Bonchi, F., Chan, T.H., Gullo, F., Sozio, M.: Finding subgraphs with maximum total density and limited overlap. In: Cheng, X., Li, H., Gabrilovich, E., Tang, J. (eds.) Proceedings of the Eighth ACM International Conference on Web Search and Data Mining, WSDM 2015, pp. 379–388. ACM (2015). https://doi.org/10.1145/2684822.2685298
Charikar, M.: Greedy approximation algorithms for finding dense components in a graph. In: Jansen, K., Khuller, S. (eds.) APPROX 2000. LNCS, vol. 1913, pp. 84–95. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44436-X_10
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press, Cambridge (2009)
Dondi, R., Hosseinzadeh, M.M., Mauri, G., Zoppis, I.: Top-k overlapping densest subgraphs: approximation and complexity. In: Proceeding in 20th Italian Conference on Theoretical Computer Science (2019, to appear)
Dondi, R., Mauri, G., Sikora, F., Zoppis, I.: Covering a graph with clubs. J. Graph Algorithms Appl. 23(2), 271–292 (2019). https://doi.org/10.7155/jgaa.00491
Fratkin, E., Naughton, B.T., Brutlag, D.L., Batzoglou, S.: MotifCut: regulatory motifs finding with maximum density subgraphs. Bioinformatics 22(14), 156–157 (2006). https://doi.org/10.1093/bioinformatics/btl243
Galbrun, E., Gionis, A., Tatti, N.: Top-k overlapping densest subgraphs. DataMin. Knowl. Discov. 30(5), 1134–1165 (2016). https://doi.org/10.1007/s10618-016-0464-z
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. WH Freeman & Co., Stuttgart (1979)
Goldberg, A.V.: Finding a Maximum Density Subgraph. University of California Berkeley, CA (1984)
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds.) Complexity of Computer Computations. IRSS, pp. 85–103. Plenum Press, New York (1972). https://doi.org/10.1007/978-1-4684-2001-2_9
Komusiewicz, C.: Multivariate algorithmics for finding cohesive subnetworks. Algorithms 9(1), 21 (2016)
Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Community structure in large networks: natural cluster sizes and the absence of large well-defined clusters. Internet Math. 6(1), 29–123 (2009). https://doi.org/10.1080/15427951.2009.10129177
Ma, X., Zhou, G., Shang, J., Wang, J., Peng, J., Han, J.: Detection of complexes in biological networks through diversified dense subgraph mining. J. Comput. Biol. 24(9), 923–941 (2017)
Mokken, R.: Cliques, clubs and clans. Qual. Quant. Int. J. Methodol. 13(2), 161–173 (1979)
Nasir, M.A.U., Gionis, A., Morales, G.D.F., Girdzijauskas, S.: Fully dynamic algorithm for top-k densest subgraphs. In: Lim, E., et al. (eds.) Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, CIKM 2017, pp. 1817–1826. ACM (2017). https://doi.org/10.1145/3132847.3132966
Rossi, R.A., Ahmed, N.K.: The network data repository with interactive graph analytics and visualization. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence (2015). http://networkrepository.com
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Hosseinzadeh, M.M. (2020). Dense Subgraphs in Biological Networks. In: Chatzigeorgiou, A., et al. SOFSEM 2020: Theory and Practice of Computer Science. SOFSEM 2020. Lecture Notes in Computer Science(), vol 12011. Springer, Cham. https://doi.org/10.1007/978-3-030-38919-2_60
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