License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.DISC.2022.26
URN: urn:nbn:de:0030-drops-172176
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17217/
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Halldórsson, Magnús M. ; Maus, Yannic ; Nolin, Alexandre

Fast Distributed Vertex Splitting with Applications

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LIPIcs-DISC-2022-26.pdf (1 MB)

Abstract

We present poly log log n-round randomized distributed algorithms to compute vertex splittings, a partition of the vertices of a graph into k parts such that a node of degree d(u) has ≈ d(u)/k neighbors in each part. Our techniques can be seen as the first progress towards general poly log log n-round algorithms for the Lovász Local Lemma.
As the main application of our result, we obtain a randomized poly log log n-round CONGEST algorithm for (1+ε)Δ-edge coloring n-node graphs of sufficiently large constant maximum degree Δ, for any ε > 0. Further, our results improve the computation of defective colorings and certain tight list coloring problems. All the results improve the state-of-the-art round complexity exponentially, even in the LOCAL model.

BibTeX - Entry

@InProceedings{halldorsson_et_al:LIPIcs.DISC.2022.26,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Maus, Yannic and Nolin, Alexandre},
  title =	{{Fast Distributed Vertex Splitting with Applications}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{26:1--26:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17217},
  URN =		{urn:nbn:de:0030-drops-172176},
  doi =		{10.4230/LIPIcs.DISC.2022.26},
  annote =	{Keywords: Graph problems, Edge coloring, List coloring, Lov\'{a}sz local lemma, LOCAL model, CONGEST model, Distributed computing}
}

Keywords: Graph problems, Edge coloring, List coloring, Lovász local lemma, LOCAL model, CONGEST model, Distributed computing
Collection: 36th International Symposium on Distributed Computing (DISC 2022)
Issue Date: 2022
Date of publication: 17.10.2022

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