Improved approximation for the directed spanner problem

Piotr Berman, Arnab Bhattacharyya, Konstantin Makarychev, Sofya Raskhodnikova, Grigory Yaroslavtsev

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

16 Scopus citations


We give an -approximation algorithm for the problem of finding the sparsest spanner of a given directed graph G on n vertices. A spanner of a graph is a sparse subgraph that approximately preserves distances in the original graph. More precisely, given a graph G∈=∈(V,E) with nonnegative edge lengths d: E → ℝ≥0 and a stretch k ≥ 1, a subgraph H = (V,E H ) is a k-spanner of G if for every edge (u,v)ε E, the graph H contains a path from u to v of length at most k •d(u,v). The previous best approximation ratio was , due to Dinitz and Krauthgamer (STOC '11). We also present an improved algorithm for the important special case of directed 3-spanners with unit edge lengths. The approximation ratio of our algorithm is which almost matches the lower bound shown by Dinitz and Krauthgamer for the integrality gap of a natural linear programming relaxation. The best previously known algorithms for this problem, due to Berman, Raskhodnikova and Ruan (FSTTCS '10) and Dinitz and Krauthgamer, had approximation ratio .

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings
Number of pages12
EditionPART 1
StatePublished - 2011
Event38th International Colloquium on Automata, Languages and Programming, ICALP 2011 - Zurich, Switzerland
Duration: Jul 4 2011Jul 8 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6755 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other38th International Colloquium on Automata, Languages and Programming, ICALP 2011

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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