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DOI: 10.4230/LIPIcs.DISC.2019.6
URN: urn:nbn:de:0030-drops-113135
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11313/
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Ben-Basat, Ran ; Kawarabayashi, Ken-ichi ; Schwartzman, Gregory

Parameterized Distributed Algorithms

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LIPIcs-DISC-2019-6.pdf (0.6 MB)


Abstract

In this work, we initiate a thorough study of graph optimization problems parameterized by the output size in the distributed setting. In such a problem, an algorithm decides whether a solution of size bounded by k exists and if so, it finds one. We study fundamental problems, including Minimum Vertex Cover (MVC), Maximum Independent Set (MaxIS), Maximum Matching (MaxM), and many others, in both the LOCAL and CONGEST distributed computation models. We present lower bounds for the round complexity of solving parameterized problems in both models, together with optimal and near-optimal upper bounds. Our results extend beyond the scope of parameterized problems. We show that any LOCAL (1+epsilon)-approximation algorithm for the above problems must take Omega(epsilon^{-1}) rounds. Joined with the (epsilon^{-1}log n)^{O(1)} rounds algorithm of [Ghaffari et al., 2017] and the Omega (sqrt{(log n)/(log log n)}) lower bound of [Fabian Kuhn et al., 2016], the lower bounds match the upper bound up to polynomial factors in both parameters. We also show that our parameterized approach reduces the runtime of exact and approximate CONGEST algorithms for MVC and MaxM if the optimal solution is small, without knowing its size beforehand. Finally, we propose the first o(n^2) rounds CONGEST algorithms that approximate MVC within a factor strictly smaller than 2.

BibTeX - Entry

@InProceedings{benbasat_et_al:LIPIcs:2019:11313,
  author =	{Ran Ben-Basat and Ken-ichi Kawarabayashi and Gregory Schwartzman},
  title =	{{Parameterized Distributed Algorithms}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Jukka Suomela},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11313},
  URN =		{urn:nbn:de:0030-drops-113135},
  doi =		{10.4230/LIPIcs.DISC.2019.6},
  annote =	{Keywords: Distributed Algorithms, Approximation Algorithms, Parameterized Algorithms}
}

Keywords: Distributed Algorithms, Approximation Algorithms, Parameterized Algorithms
Seminar: 33rd International Symposium on Distributed Computing (DISC 2019)
Issue Date: 2019
Date of publication: 11.10.2019


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