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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.OPODIS.2017.5
URN: urn:nbn:de:0030-drops-86262
URL: http://drops.dagstuhl.de/opus/volltexte/2018/8626/
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Dinitz, Michael ; Nazari, Yasamin

Distributed Distance-Bounded Network Design Through Distributed Convex Programming

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LIPIcs-OPODIS-2017-5.pdf (0.6 MB)


Abstract

Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al. 2006), this is essentially the only class of linear programs for which such an algorithm is known. In this work we provide a distributed algorithm for solving a different class of convex programs which we call “distance-bounded network design convex programs”. These can be thought of as relaxations of network design problems in which the connectivity requirement includes a distance constraint (most notably, graph spanners). Our algorithm runs in O((D/&#949;) log n) rounds in the LOCAL model and with high probability finds a (1+&#949;)-approximation to the optimal LP solution for any 0 < &#949; &#8804; 1, where D is the largest distance constraint. While solving linear programs in a distributed setting is interesting in its own right, this class of convex programs is particularly important because solving them is often a crucial step when designing approximation algorithms. Hence we almost immediately obtain new and improved distributed approximation algorithms for a variety of network design problems, including Basic 3- and 4-Spanner, Directed k-Spanner, Lowest Degree k-Spanner, and Shallow-Light Steiner Network Design with a spanning demand graph. Our algorithms do not require any “heavy” computation and essentially match the best-known centralized approximation algorithms, while previous approaches which do not use heavy computation give approximations which are worse than the best-known centralized bounds.

BibTeX - Entry

@InProceedings{dinitz_et_al:LIPIcs:2018:8626,
  author =	{Michael Dinitz and Yasamin Nazari},
  title =	{{Distributed Distance-Bounded Network Design Through Distributed Convex Programming}},
  booktitle =	{21st International Conference on Principles of Distributed Systems (OPODIS 2017)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-061-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{95},
  editor =	{James Aspnes and Alysson Bessani and Pascal Felber and Jo{\~a}o Leit{\~a}o},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8626},
  URN =		{urn:nbn:de:0030-drops-86262},
  doi =		{10.4230/LIPIcs.OPODIS.2017.5},
  annote =	{Keywords: distributed algorithms, approximation algorithms, convex programming}
}

Keywords: distributed algorithms, approximation algorithms, convex programming
Seminar: 21st International Conference on Principles of Distributed Systems (OPODIS 2017)
Issue Date: 2018
Date of publication: 16.03.2018


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