Fault tolerant additive spanners

Gilad Braunschvig, Shiri Chechik, David Peleg

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

15 Scopus citations


Graph spanners are sparse subgraphs that preserve the distances of the original graph, up to some small multiplicative factor or additive term (known as the stretch of the spanner). A number of algorithms are known for constructing sparse spanners with small multiplicative or additive stretch. Recently, the problem of constructing fault-tolerant multiplicative spanners for general graphs was given some algorithms. This paper addresses the analogous problem of constructing fault tolerant additive spanners for general graphs. We establish the following general result. Given an n-vertex graph G, if H 1 is an ordinary additive spanner for G with additive stretch α, and H 2 is a fault tolerant multiplicative spanner for G, resilient against up to f edge failures, with multiplicative stretch μ, then H∈=∈H 1∈∪∈H 2 is an additive fault tolerant spanner of G, resilient against up to f edge failures, with additive stretch where is the number of failures that have actually occurred. This allows us to derive a poly-time algorithm for constructing an additive fault tolerant spanner H of G, relying on the existence of algorithms for constructing fault tolerant multiplicative spanners and (ordinary) additive spanners. In particular, based on some known spanner construction algorithms, we show how to construct for any n-vertex graph G an additive fault tolerant spanner with additive stretch and size O(fn 4/3).

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 38th International Workshop, WG 2012, Revised Selcted Papers
Number of pages9
StatePublished - 2012
Externally publishedYes
Event38th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2012 - Jerusalem, Israel
Duration: 26 Jun 201228 Jun 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7551 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference38th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2012


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