Alternative Parameterizations for Cluster Editing
Given an undirected graph G and a nonnegative integer k, the NP-hard Cluster Editing problem asks whether G can be transformed into a disjoint union of cliques by applying at most k edge modifications. In the field of parameterized algorithmics, Cluster Editing has almost exclusively been studied parameterized by the solution size k. Contrastingly, in many real-world instances it can be observed that the parameter k is not really small. This observation motivates our investigation of parameterizations of Cluster Editing different from the solution size k. Our results are as follows. Cluster Editing is fixed-parameter tractable with respect to the parameter “size of a minimum cluster vertex deletion set of G”, a typically much smaller parameter than k. Cluster Editing remains NP-hard on graphs with maximum degree six. A restricted but practically relevant version of Cluster Editing is fixed-parameter tractable with respect to the combined parameter “number of clusters in the target graph” and “maximum number of modified edges incident to any vertex in G”. Many of our results also transfer to the NP-hard Cluster Deletion problem, where only edge deletions are allowed.
KeywordsEdit Distance Reduction Rule Cluster Graph Edge Deletion Solution Size
Unable to display preview. Download preview PDF.
- 3.Böcker, S., Briesemeister, S., Klau, G.W.: Exact algorithms for cluster editing: Evaluation and experiments. Algorithmica (2009) (to appear)Google Scholar
- 7.Demaine, E.D., Hajiaghayi, M., Marx, D.: Open problems – parameterized complexity and approximation algorithms. In: Parameterized Complexity and Approximation Algorithms. Dagstuhl Seminar Proceedings, vol. 09511. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany (2010)Google Scholar
- 12.Guo, J., Komusiewicz, C., Niedermeier, R., Uhlmann, J.: A more relaxed model for graph-based data clustering: s-plex cluster editing. SIAM Journal on Discrete Mathematics (2010) (to appear)Google Scholar
- 15.Niedermeier, R.: Reflections on multivariate algorithmics and problem parameterization. In: Proc. 27th STACS, vol. 5, pp. 17–32. Schloss Dagstuhl–Leibniz-Zentrum für Informatik, LIPIcs (2010)Google Scholar