Abstract
We introduce the s -Plex Editing problem generalizing the well-studied Cluster Editing problem, both being NP-hard and both being motivated by graph-based data clustering. Instead of transforming a given graph by a minimum number of edge modifications into a disjoint union of cliques (Cluster Editing), the task in the case of s -Plex Editing is now to transform a graph into a disjoint union of so-called s-plexes. Herein, an s-plex denotes a vertex set inducing a (sub)graph where every vertex has edges to all but at most s vertices in the s-plex. Cliques are 1-plexes. The advantage of s-plexes for s ≥ 2 is that they allow to model a more relaxed cluster notion (s-plexes instead of cliques), which better reflects inaccuracies of the input data. We develop a provably efficient and effective preprocessing based on data reduction (yielding a so-called problem kernel), a forbidden subgraph characterization of s-plex cluster graphs, and a depth-bounded search tree which is used to find optimal edge modification sets. Altogether, this yields efficient algorithms in case of moderate numbers of edge modifications.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Balasundaram, B., Butenko, S., Hicks, I.V., Sachdeva, S.: Clique relaxations in social network analysis: The maximum k-plex problem (manuscript, 2006)
Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Machine Learning 56(1-3), 89–113 (2004)
Böcker, S., Briesemeister, S., Bui, Q.B.A., Truß, A.: Going weighted: Parameterized algorithms for cluster editing. In: Yang, B., Du, D.-Z., Wang, C.A. (eds.) COCOA 2008. LNCS, vol. 5165, pp. 1–12. Springer, Heidelberg (2008)
Böcker, S., Briesemeister, S., Klau, G.W.: Exact algorithms for cluster editing: Evaluation and experiments. In: McGeoch, C.C. (ed.) WEA 2008. LNCS, vol. 5038, pp. 289–302. Springer, Heidelberg (2008)
Chesler, E.J., Lu, L., Shou, S., Qu, Y., Gu, J., Wang, J., Hsu, H.C., Mountz, J.D., Baldwin, N.E., Langston, M.A., Threadgill, D.W., Manly, K.F., Williams, R.W.: Complex trait analysis of gene expression uncovers polygenic and pleiotropic networks that modulate nervous system function. Nature Genetics 37(3), 233–242 (2005)
Cook, V.J., Sun, S.J., Tapia, J., Muth, S.Q., Argüello, D.F., Lewis, B.L., Rothenberg, R.B., McElroy, P.D., The Network Analysis Project Team: Transmission network analysis in tuberculosis contact investigations. Journal of Infectious Diseases 196, 1517–1527 (2007)
Fellows, M.R., Langston, M.A., Rosamond, F.A., Shaw, P.: Efficient parameterized preprocessing for cluster editing. In: Csuhaj-Varjú, E., Ésik, Z. (eds.) FCT 2007. LNCS, vol. 4639, pp. 312–321. Springer, Heidelberg (2007)
Guo, J.: A more effective linear kernelization for Cluster Editing. Theoretical Computer Science 410(8), 718–726 (2009)
Guo, J., Niedermeier, R.: Invitation to data reduction and problem kernelization. ACM SIGACT News 38(1), 31–45 (2007)
Komusiewicz, C., Hüffner, F., Moser, H., Niedermeier, R.: Isolation concepts for enumerating dense subgraphs. In: Lin, G. (ed.) COCOON 2007. LNCS, vol. 4598, pp. 140–150. Springer, Heidelberg (2007)
Memon, N., Kristoffersen, K.C., Hicks, D.L., Larsen, H.L.: Detecting critical regions in covert networks: A case study of 9/11 terrorists network. In: Proc. 2nd ARES, pp. 861–870. IEEE Computer Society, Los Alamitos (2007)
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford Lecture Series in Mathematics and Its Applications, vol. 31. Oxford University Press, Oxford (2006)
Seidman, S.B., Foster, B.L.: A graph-theoretic generalization of the clique concept. Journal of Mathematical Sociology 6, 139–154 (1978)
Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. Discrete Applied Mathematics 144(1–2), 173–182 (2004)
Tarjan, R.E.: Depth-first search and linear graph algorithms. SIAM Journal on Computing 1(2), 146–160 (1972)
Xu, R., Wunsch II, D.: Survey of clustering algorithms. IEEE Transactions on Neural Networks 16(3), 645–678 (2005)
van Zuylen, A., Williamson, D.P.: Deterministic algorithms for rank aggregation and other ranking and clustering problems. In: Kaklamanis, C., Skutella, M. (eds.) WAOA 2007. LNCS, vol. 4927, pp. 260–273. Springer, Heidelberg (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Guo, J., Komusiewicz, C., Niedermeier, R., Uhlmann, J. (2009). A More Relaxed Model for Graph-Based Data Clustering: s-Plex Editing. In: Goldberg, A.V., Zhou, Y. (eds) Algorithmic Aspects in Information and Management. AAIM 2009. Lecture Notes in Computer Science, vol 5564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02158-9_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-02158-9_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02157-2
Online ISBN: 978-3-642-02158-9
eBook Packages: Computer ScienceComputer Science (R0)