Transitive-closure spanners: A survey

Sofya Raskhodnikova

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

20 Scopus citations


We survey results on transitive-closure spanners and their applications. Given a directed graph G = (V,E) and an integer k ≥ 1, a k-transitive- closure-spanner (k-TC-spanner) of G is a directed graph H = (V, EH ) that has (1) the same transitive-closure as G and (2) diameter at most k. These spanners were studied implicitly in different areas of computer science, and properties of these spanners have been rediscovered over the span of 20 years. The common task implicitly tackled in these diverse applications can be abstracted as the problem of constructing sparse TC-spanners. In this article, we survey combinatorial bounds on the size of sparsest TC-spanners, and algorithms and inapproximability results for the problem of computing the sparsest TC-spanner of a given directed graph. We also describe multiple applications of TC-spanners, including property testing, property reconstruction, key management in access control hierarchies and data structures.

Original languageEnglish (US)
Title of host publicationProperty Testing - Current Research and Surveys
Number of pages30
StatePublished - Nov 24 2010
EventMini-Workshop on Property Testing - Beijing, China
Duration: Jan 8 2010Jan 10 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6390 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


OtherMini-Workshop on Property Testing

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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