Roundtrip spanners and roundtrip routing in directed graphs

Liam Roditty, Mikkel Thorup, Uri Zwick

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

24 Scopus citations

Abstract

We introduce the notion of roundtrip-spanners of weighted directed graphs and describe efficient algorithms for their construction. For every integer k ≥ 1 and any ϵ > 0, we show that any directed graph on n vertices with edge weights in the range [1,W] has a (2k + e)-roundtrip-spanner with O(k2/ϵn1+1/k log(nW)) edges. We then extend these constructions and obtain compact roundtrip routing schemes. For every integer k > 1 and every ϵ > 0, we describe a roundtrip routing scheme that has stretch 4k + ϵ, and uses at each vertex a routing table of size O(k2/ϵ n1k log(n.W)). We also show that any weighted directed graph with arbitrary positive edge weights has a 3-roundtrip-spanner with O(n3/2) edges. This result is optimal. Finally, we present a stretch 3 roundtrip routing scheme that uses local routing tables of size O(n1/2). This routing scheme is essentially optimal. The roundtrip-spanner constructions and the roundtrip routing schemes for directed graphs that we describe are only slightly worse than the best available spanners and routing schemes for undirected graphs. Our roundtrip routing schemes substantially improve previous results of Cowen and Wagner. Our results are obtained by combining ideas of Cohen, Cowen and Wagner, Thorup and Zwick, with some new ideas.

Original languageEnglish
Title of host publicationProceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002
PublisherAssociation for Computing Machinery
Pages844-851
Number of pages8
ISBN (Electronic)089871513X
StatePublished - 2002
Event13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 - San Francisco, United States
Duration: 6 Jan 20028 Jan 2002

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume06-08-January-2002

Conference

Conference13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002
Country/TerritoryUnited States
CitySan Francisco
Period6/01/028/01/02

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