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.ESA.2017.7
URN: urn:nbn:de:0030-drops-78268
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7826/
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Albers, Susanne ; Schraink, Sebastian

Tight Bounds for Online Coloring of Basic Graph Classes

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LIPIcs-ESA-2017-7.pdf (0.5 MB)

Abstract

We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our bounds also hold for randomized online algorithms, for which hardly any results were known. Technically, we construct lower bounds for chordal graphs. The constructions then allow us to derive results on the performance of randomized online algorithms for the following further graph classes: trees, planar, bipartite, inductive, bounded-treewidth and disk graphs. It shows that the best competitive ratio of both deterministic and randomized online algorithms is Theta(log n), where n is the number of vertices of a graph. Furthermore, we prove that this guarantee cannot be improved if an online algorithm has a lookahead of size O(n/log n) or access to a reordering buffer of size n^(1-epsilon), for any 0 < epsilon <= 1. A consequence of our results is that, for all of the above mentioned graph classes except bipartite graphs, the natural First Fit coloring algorithm achieves an optimal performance, up to constant factors, among deterministic and randomized
online algorithms.

BibTeX - Entry

@InProceedings{albers_et_al:LIPIcs:2017:7826,
  author =	{Susanne Albers and Sebastian Schraink},
  title =	{{Tight Bounds for Online Coloring of Basic Graph Classes}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Kirk Pruhs and Christian Sohler},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7826},
  URN =		{urn:nbn:de:0030-drops-78268},
  doi =		{10.4230/LIPIcs.ESA.2017.7},
  annote =	{Keywords: graph coloring, online algorithms, lower bounds, randomization}
}

Keywords: graph coloring, online algorithms, lower bounds, randomization
Collection: 25th Annual European Symposium on Algorithms (ESA 2017)
Issue Date: 2017
Date of publication: 01.09.2017

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