eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-11-19
402
413
10.4230/LIPIcs.IPEC.2015.402
article
Fast Biclustering by Dual Parameterization
Drange, Pål Grønås
Reidl, Felix
Sánchez Villaamil, Fernando
Sikdar, Somnath
We study two clustering problems, Starforest Editing, the problem of adding and deleting edges to obtain a disjoint union of stars, and the generalization Bicluster Editing. We show that, in addition to being NP-hard, none of the problems can be solved in subexponential time unless the exponential time hypothesis fails.
Misra, Panolan, and Saurabh (MFCS 2013) argue that introducing a bound on the number of connected components in the solution should not make the problem easier: In particular, they argue that the subexponential time algorithm for editing to a fixed number of clusters (p-Cluster Editing) by Fomin et al. (J. Comput. Syst. Sci., 80(7) 2014) is an exception rather than the rule. Here, p is a secondary parameter, bounding the number of components in the solution.
However, upon bounding the number of stars or bicliques in the solution, we obtain algorithms which run in time O(2^{3*sqrt(pk)} + n + m) for p-Starforest Editing and O(2^{O(p * sqrt(k) * log(pk))} + n + m) for p-Bicluster Editing. We obtain a similar result for the more general case of t-Partite p-Cluster Editing. This is subexponential in k for a fixed number of clusters, since p is then considered a constant.
Our results even out the number of multivariate subexponential time algorithms and give reasons to believe that this area warrants further study.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol043-ipec2015/LIPIcs.IPEC.2015.402/LIPIcs.IPEC.2015.402.pdf
graph editing
subexponential algorithms
parameterized complexity