Finding sparser directed spanners

Piotr Berman, Sofya Raskhodnikova, Ge Ruan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

A spanner of a graph is a sparse subgraph that approximately preserves distances in the original graph. More precisely, a subgraph H = (V,E H) is a k-spanner of a graph G = (V,E) if for every pair of vertices u, v ∈ V, the shortest path distance distH(u,v) from u to v in H is at most k · distc(u, v). We focus on spanners of directed graphs and a related notion of transitive-closure spanners. The latter captures the idea that a spanner should have a small diameter but preserve the connectivity of the original graph. We study the computational problem of finding the sparsest k-spanner (resp., k-TC-spanner) of a given directed graph, which we refer to as DIRECTED k-SPANNER (resp., k-TC-SPANNER). We improve all known approximation algorithms for DIRECTED k-SPANNER and k-TC-SPANNER for k ≥ 3. (For k = 2, the current ratios are tight, assuming P≠NP.) Along the way, we prove several structural results about the size of the sparsest spanners of directed graphs.

Original languageEnglish (US)
Title of host publication30th International Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010
Pages424-435
Number of pages12
DOIs
StatePublished - Dec 1 2010
Event30th Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010 - Chennai, India
Duration: Dec 15 2010Dec 18 2010

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume8
ISSN (Print)1868-8969

Other

Other30th Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010
CountryIndia
CityChennai
Period12/15/1012/18/10

All Science Journal Classification (ASJC) codes

  • Software

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