Fast Biclustering by Dual Parameterization
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.
graph editing
subexponential algorithms
parameterized complexity
402-413
Regular Paper
Pål Grønås
Drange
Pål Grønås Drange
Felix
Reidl
Felix Reidl
Fernando
Sánchez Villaamil
Fernando Sánchez Villaamil
Somnath
Sikdar
Somnath Sikdar
10.4230/LIPIcs.IPEC.2015.402
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode