License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.28
URN: urn:nbn:de:0030-drops-63078
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6307/
Marx, Dániel ;
Mitsou, Valia
Double-Exponential and Triple-Exponential Bounds for Choosability Problems Parameterized by Treewidth
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}
}
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Keywords: |
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Parameterized Complexity, List coloring, Treewidth, Lower bounds under ETH |
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Collection: |
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43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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23.08.2016 |
