On the hardness of approximating spanners

Guy Kortsarz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


A k-spanner of a connected graph G = (V, E) is a subgraph Gʹ consisting of all the vertices of V and a subset of the edges, with the additional property that the distance between any two vertices in Gʹ is larger than that distance in G by no more than a factor of k. This paper concerns the hardness of finding spanners with the number of edges close to the optimum. It is proved that for every fixed k approximating the spanner problem is at least as hard as approximating the set cover problem We also consider a weighted version of the spanner problem. We prove that in the case k = 2 the problem admits an O(log n)-ratio approximation, and in the case k ≥ 5, there is no 2log1-ϵ n-ratio approximation, for any ϵ > 0, unless NP ⊆ DTIME(npolylog n).

Original languageEnglish
Title of host publicationApproximation Algorithms for Combinatorial Optimization - International Workshop, APPROX 1998, Proceedings
EditorsJosé Rolim, Klaus Jansen
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540647368, 9783540647362
StatePublished - 1998
EventInternational Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 1998 - Aalborg, Denmark
Duration: 18 Jul 199819 Jul 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceInternational Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 1998

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1998.


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