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.STACS.2015.513
URN: urn:nbn:de:0030-drops-49381
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/4938/
Go to the corresponding LIPIcs Volume Portal

Kavitha, Telikepalli

New Pairwise Spanners

pdf-format:
38.pdf (0.6 MB)

Abstract

Let G = (V,E) be an undirected unweighted graph on n vertices. A subgraph H of G is called an (all-pairs) purely additive spanner with stretch \beta if for every (u,v) \in V \times V, \mathsf{dist}_H(u,v) \le \mathsf{dist}_G(u,v) + \beta. The problem of computing sparse spanners with small stretch \beta is well-studied. Here we consider the following relaxation: we are given \p\subseteq V \times V and we seek a sparse subgraph H where \mathsf{dist}_H(u,v)\le \mathsf{dist}_G(u,v) + \beta for each (u,v) \in \p. Such a subgraph is called a pairwise spanner with additive stretch \beta and our goal is to construct
such subgraphs that are sparser than all-pairs spanners with the same stretch. We show sparse pairwise spanners with additive stretch 4 and with additive stretch 6. We also consider the following special cases: \p = S \times V and \p = S \times T, where S\subseteq V and T\subseteq V, and show sparser pairwise spanners for these cases.

BibTeX - Entry

@InProceedings{kavitha:LIPIcs:2015:4938,
  author =	{Telikepalli Kavitha},
  title =	{{New Pairwise Spanners}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{513--526},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Ernst W. Mayr and Nicolas Ollinger},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/4938},
  URN =		{urn:nbn:de:0030-drops-49381},
  doi =		{10.4230/LIPIcs.STACS.2015.513},
  annote =	{Keywords: undirected graphs, spanners, approximate distances, additive stretch}
}

Keywords: undirected graphs, spanners, approximate distances, additive stretch
Collection: 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)
Issue Date: 2015
Date of publication: 26.02.2015

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI