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.DISC.2019.4
URN: urn:nbn:de:0030-drops-113116
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11311/
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Becker, Ruben ; Emek, Yuval ; Ghaffari, Mohsen ; Lenzen, Christoph

Distributed Algorithms for Low Stretch Spanning Trees

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LIPIcs-DISC-2019-4.pdf (0.6 MB)

Abstract

Given an undirected graph with integer edge lengths, we study the problem of approximating the distances in the graph by a spanning tree based on the notion of stretch. Our main contribution is a distributed algorithm in the CONGEST model of computation that constructs a random spanning tree with the guarantee that the expected stretch of every edge is O(log^{3} n), where n is the number of nodes in the graph. If the graph is unweighted, then this algorithm can be implemented to run in O(D) rounds, where D is the hop-diameter of the graph, thus being asymptotically optimal. In the weighted case, the run-time of our algorithm matches the currently best known bound for exact distance computations, i.e., O~ (min{sqrt{n D}, sqrt{n} D^{1 / 4} + n^{3 / 5} + D}). We stress that this is the first distributed construction of spanning trees leading to poly-logarithmic expected stretch with non-trivial running time.

BibTeX - Entry

@InProceedings{becker_et_al:LIPIcs:2019:11311,
  author =	{Ruben Becker and Yuval Emek and Mohsen Ghaffari and Christoph Lenzen},
  title =	{{Distributed Algorithms for Low Stretch Spanning Trees}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{4:1--4:14},
  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/2019/11311},
  URN =		{urn:nbn:de:0030-drops-113116},
  doi =		{10.4230/LIPIcs.DISC.2019.4},
  annote =	{Keywords: distributed graph algorithms, low-stretch spanning trees, CONGEST model, ball decomposition, star decomposition}
}

Keywords: distributed graph algorithms, low-stretch spanning trees, CONGEST model, ball decomposition, star decomposition
Collection: 33rd International Symposium on Distributed Computing (DISC 2019)
Issue Date: 2019
Date of publication: 08.10.2019

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