2026-07-23T12:53:56Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:4938 2024-03-06T10:35:35Z ddc:004 open_access

New Pairwise Spanners Kavitha, Telikepalli undirected graphs spanners approximate distances additive stretch 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Telikepalli Kavitha 2015 Is Part Of LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2015.513 urn:nbn:de:0030-drops-49381 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.513 eng https://creativecommons.org/licenses/by/3.0/legalcode