Steiner transitive-closure spanners of low-dimensional posets

Piotr Berman, Arnab Bhattacharyya, Elena Grigorescu, Sofya Raskhodnikova, David P. Woodruff, Grigory Yaroslavtsev

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

4 Scopus citations

Abstract

Given a directed graph G = (V,E) and an integer k ≥ 1, a Steiner k -transitive-closure-spanner (Steiner k-TC-spanner) of G is a directed graph H = (V H , E H ) such that (1) V ⊆ V H and (2) for all vertices v,u ε V, the distance from v to u in H is at most k if u is reachable from v in G, and ∞ otherwise. Motivated by applications to property reconstruction and access control hierarchies, we concentrate on Steiner TC-spanners of directed acyclic graphs or, equivalently, partially ordered sets. We study the relationship between the dimension of a poset and the size, denoted S k , of its sparsest Steiner k-TC-spanner. We present a nearly tight lower bound on S 2 for d-dimensional directed hypergrids. Our bound is derived from an explicit dual solution to a linear programming relaxation of the 2-TC-spanner problem. We also give an efficient construction of Steiner 2-TC-spanners, of size matching the lower bound, for all low-dimensional posets. Finally, we present a nearly tight lower bound on S k for d-dimensional posets.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings
Pages760-772
Number of pages13
EditionPART 1
DOIs
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

Other

Other38th International Colloquium on Automata, Languages and Programming, ICALP 2011
CountrySwitzerland
CityZurich
Period7/4/117/8/11

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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