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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2016.58
URN: urn:nbn:de:0030-drops-64001
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6400/
Kowalik, Lukasz ;
Lauri, Juho ;
Socala, Arkadiusz
On the Fine-Grained Complexity of Rainbow Coloring
Abstract
The Rainbow k-Coloring problem asks whether the edges of a given graph can be colored in k colors so that every pair of vertices is connected by a rainbow path, i.e., a path with all edges of different colors. Our main result states that for any k >= 2, there is no algorithm for Rainbow k-Coloring running in time 2^{o(n^{3/2})}, unless ETH fails. Motivated by this negative result we consider two parameterized variants of the problem. In the Subset Rainbow k-Coloring problem, introduced by Chakraborty et al. [STACS 2009, J. Comb. Opt. 2009], we are additionally given a set S of pairs of vertices and we ask if there is a coloring in which all the pairs in S are connected by rainbow paths. We show that Subset Rainbow k-Coloring is FPT when parameterized by |S|. We also study Subset Rainbow k-Coloring problem, where we are additionally given an integer q and we ask if there is a coloring in which at least q anti-edges are connected by rainbow paths. We show that the problem is FPT when parameterized by q and has a kernel of size O(q) for every k >= 2, extending the result of Ananth et al. [FSTTCS 2011]. We believe that our techniques used for the lower bounds may shed some light on the complexity of the classical Edge Coloring problem, where it is a major open question if a 2^{O(n)}-time algorithm exists.
BibTeX - Entry
@InProceedings{kowalik_et_al:LIPIcs:2016:6400,
author = {Lukasz Kowalik and Juho Lauri and Arkadiusz Socala},
title = {{On the Fine-Grained Complexity of Rainbow Coloring}},
booktitle = {24th Annual European Symposium on Algorithms (ESA 2016)},
pages = {58:1--58:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-015-6},
ISSN = {1868-8969},
year = {2016},
volume = {57},
editor = {Piotr Sankowski and Christos Zaroliagis},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6400},
URN = {urn:nbn:de:0030-drops-64001},
doi = {10.4230/LIPIcs.ESA.2016.58},
annote = {Keywords: graph coloring, computational complexity, lower bounds, exponential time hypothesis, FPT algorithms}
}
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Keywords: |
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graph coloring, computational complexity, lower bounds, exponential time hypothesis, FPT algorithms |
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Collection: |
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24th Annual European Symposium on Algorithms (ESA 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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18.08.2016 |
