Local computation of nearly additive spanners

Bilel Derbel, Cyril Gavoille, David Peleg, Laurent Viennot

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

15 Scopus citations


An (α,β)-spanner of a graph G is a subgraph H that approximates distances in G within a multiplicative factor α and an additive error β, ensuring that for any two nodes u,v, d H (u,v) ≤α•d G (u,v)+β. This paper concerns algorithms for the distributed deterministic construction of a sparse (α,β)-spanner H for a given graph G and distortion parameters α and β. It first presents a generic distributed algorithm that in constant number of rounds constructs, for every n-node graph and integer kge;1, an (α,β)- spanner of O(βn 1+1/k ) edges, where α and β are constants depending on k. For suitable parameters, this algorithm provides a (2k-1,0)-spanner of at most k n 1+1/k edges in k rounds, matching the performances of the best known distributed algorithm by Derbel et al. (PODC '08). For k=2 and constant ε>0, it can also produce a (1+ε,2-ε)-spanner of O(n 3/2) edges in constant time. More interestingly, for every integer k>1, it can construct in constant time a (1+ε,O(1/ε) k-2)-spanner of O(ε -k+1 n 1+1/k ) edges. Such deterministic construction was not previously known. The paper also presents a second generic deterministic and distributed algorithm based on the construction of small dominating sets and maximal independent sets. After computing such sets in sub-polynomial time, it constructs at its best a (1+ε,β)-spanner with O(βn 1+1/k ) edges, where β=k log(logk/ε)+O(1). For k=3, it provides a (1+ε, 6-ε)-spanner with O(ε -1 n 4/3) edges. The additive terms β=β(k,ε) in the stretch of our constructions yield the best trade-off currently known between k and ε, due to Elkin and Peleg (STOC '01). Our distributed algorithms are rather short, and can be viewed as a unification and simplification of previous constructions.

Original languageEnglish
Title of host publicationDistributed Computing - 23rd International Symposium, DISC 2009, Proceedings
PublisherSpringer Verlag
Number of pages15
ISBN (Print)3642043542, 9783642043543
StatePublished - 2009
Externally publishedYes
Event23rd International Symposium on Distributed Computing, DISC 2009 - Elche, Spain
Duration: 23 Sep 200925 Sep 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5805 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference23rd International Symposium on Distributed Computing, DISC 2009


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