Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Henzinger, Monika; Peng, Pan https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-119145
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Constant-Time Dynamic (Δ+1)-Coloring

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Abstract

We give a fully dynamic (Las-Vegas style) algorithm with constant expected amortized time per update that maintains a proper (Δ+1)-vertex coloring of a graph with maximum degree at most Δ. This improves upon the previous O(log Δ)-time algorithm by Bhattacharya et al. (SODA 2018). Our algorithm uses an approach based on assigning random ranks to vertices and does not need to maintain a hierarchical graph decomposition. We show that our result does not only have optimal running time, but is also optimal in the sense that already deciding whether a Δ-coloring exists in a dynamically changing graph with maximum degree at most Δ takes Ω(log n) time per operation.

BibTeX - Entry

@InProceedings{henzinger_et_al:LIPIcs:2020:11914,
  author =	{Monika Henzinger and Pan Peng},
  title =	{{Constant-Time Dynamic (Δ+1)-Coloring}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{53:1--53:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Christophe Paul and Markus Bl{\"a}ser},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11914},
  URN =		{urn:nbn:de:0030-drops-119145},
  doi =		{10.4230/LIPIcs.STACS.2020.53},
  annote =	{Keywords: Dynamic graph algorithms, Graph coloring, Random sampling}
}

Keywords: Dynamic graph algorithms, Graph coloring, Random sampling
Seminar: 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)
Issue date: 2020
Date of publication: 04.03.2020


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