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DOI: 10.4230/LIPIcs.ICALP.2016.28
URN: urn:nbn:de:0030-drops-63078
URL: http://drops.dagstuhl.de/opus/volltexte/2016/6307/
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Marx, Dániel ; Mitsou, Valia

Double-Exponential and Triple-Exponential Bounds for Choosability Problems Parameterized by Treewidth

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Abstract

Choosability, introduced by Erdös, Rubin, and Taylor [Congr. Number. 1979], is a well-studied concept in graph theory: we say that a graph is c-choosable if for any assignment of a list of c colors to each vertex, there is a proper coloring where each vertex uses a color from its list. We study the complexity of deciding choosability on graphs of bounded treewidth. It follows from earlier work that 3-choosability can be decided in time 2^(2^(O(w)))*n^(O(1)) on graphs of treewidth w. We complement this result by a matching lower bound giving evidence that double-exponential dependence on treewidth may be necessary for the problem: we show that an algorithm with running time 2^(2^(o(w)))*n^(O(1)) would violate the Exponential-Time Hypothesis (ETH). We consider also the optimization problem where the task is to delete the minimum number of vertices to make the graph 4-choosable, and demonstrate that dependence on treewidth becomes tripleexponential for this problem: it can be solved in time 2^(2^(2^(O(w))))*n^(O(1)) on graphs of treewidth w, but an algorithm with running time 2^(2^(2^(o(w))))*n^(O(1)) would violate ETH.

BibTeX - Entry

@InProceedings{marx_et_al:LIPIcs:2016:6307,
  author =	{D{\'a}niel Marx and Valia Mitsou},
  title =	{{Double-Exponential and Triple-Exponential Bounds for Choosability Problems Parameterized by Treewidth}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6307},
  URN =		{urn:nbn:de:0030-drops-63078},
  doi =		{10.4230/LIPIcs.ICALP.2016.28},
  annote =	{Keywords: Parameterized Complexity, List coloring, Treewidth, Lower bounds under ETH}
}

Keywords: Parameterized Complexity, List coloring, Treewidth, Lower bounds under ETH
Seminar: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 17.08.2016


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