License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.IPEC.2015.402
URN: urn:nbn:de:0030-drops-56004
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Drange, Pål Grønås ; Reidl, Felix ; Sánchez Villaamil, Fernando ; Sikdar, Somnath

Fast Biclustering by Dual Parameterization

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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.

BibTeX - Entry

  author =	{Pål Gr\onås Drange and Felix Reidl and Fernando S{\'a}nchez Villaamil and Somnath Sikdar},
  title =	{{Fast Biclustering by Dual Parameterization}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{402--413},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-92-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{43},
  editor =	{Thore Husfeldt and Iyad Kanj},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-56004},
  doi =		{10.4230/LIPIcs.IPEC.2015.402},
  annote =	{Keywords: graph editing, subexponential algorithms, parameterized complexity}

Keywords: graph editing, subexponential algorithms, parameterized complexity
Collection: 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)
Issue Date: 2015
Date of publication: 19.11.2015

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