A More Relaxed Model for Graph-Based Data Clustering: s-Plex Editing
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.
KeywordsSearch Tree Input Graph Reduction Rule Cluster Graph Relax Model
Unable to display preview. Download preview PDF.
- 1.Balasundaram, B., Butenko, S., Hicks, I.V., Sachdeva, S.: Clique relaxations in social network analysis: The maximum k-plex problem (manuscript, 2006)Google Scholar
- 5.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)CrossRefGoogle Scholar
- 6.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)Google Scholar
- 11.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)Google Scholar