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DOI: 10.4230/LIPIcs.IPEC.2015.78
URN: urn:nbn:de:0030-drops-55738
URL: https://drops.dagstuhl.de/opus/volltexte/2015/5573/
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Kim, Eun Jung ; Paul, Christophe ; Sau, Ignasi ; Thilikos, Dimitrios M.

Parameterized Algorithms for Min-Max Multiway Cut and List Digraph Homomorphism

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Abstract

In this paper we design FPT-algorithms for two parameterized problems. The first is List Digraph Homomorphism: given two digraphs G and H and a list of allowed vertices of H for every vertex of G, the question is whether there exists a homomorphism from G to H respecting the list constraints. The second problem is a variant of Multiway Cut, namely Min-Max Multiway Cut: given a graph G, a non-negative integer l, and a set T of r terminals, the question is whether we can partition the vertices of G into r parts such that (a) each part contains one terminal and (b) there are at most l edges with only one endpoint in this part. We parameterize List Digraph Homomorphism by the number w of edges of G that are mapped to non-loop edges of H and we give a time 2^{O(l * log(h) + l^{2 * log(l)}} * n^{4} * log(n) algorithm, where h is the order of the host graph H.We also prove that Min-Max Multiway Cut can be solved in time 2^{O((l * r)^2 * log(l *r))} * n^{4} * log(n). Our approach introduces a general problem, called List Allocation, whose expressive power permits the design of parameterized reductions of both aforementioned problems to it. Then our results are based on an FPT-algorithm for the List Allocation problem that is designed using a suitable adaptation of the randomized contractions technique (introduced by [Chitnis, Cygan, Hajiaghayi, Pilipczuk, and Pilipczuk, FOCS 2012]).

BibTeX - Entry

@InProceedings{kim_et_al:LIPIcs:2015:5573,
  author =	{Eun Jung Kim and Christophe Paul and Ignasi Sau and Dimitrios M. Thilikos},
  title =	{{Parameterized Algorithms for Min-Max Multiway Cut and List Digraph Homomorphism}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{78--89},
  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 =		{http://drops.dagstuhl.de/opus/volltexte/2015/5573},
  URN =		{urn:nbn:de:0030-drops-55738},
  doi =		{10.4230/LIPIcs.IPEC.2015.78},
  annote =	{Keywords: Parameterized complexity, Fixed-Parameter Tractable algorithm, Multiway Cut, Digraph homomorphism}
}

Keywords: Parameterized complexity, Fixed-Parameter Tractable algorithm, Multiway Cut, Digraph homomorphism
Seminar: 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)
Issue Date: 2015
Date of publication: 09.11.2015


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