Optimal Reachability and a Space-Time Tradeoff for Distance Queries in Constant-Treewidth Graphs

Krishnendu Chatterjee, Rasmus Rasmus Ibsen-Jensen, Andreas Pavlogiannis

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review

Abstract

We consider data-structures for answering reachability and distance queries on constant-treewidth graphs with n nodes, on the standard RAM computational model with wordsize W = Θ(log n). Our first contribution is a data-structure that after O(n) preprocessing time, allows (1) pair reachability queries in O(1) time; and (2) single-source reachability queries in O(n/log n) time. This is (asymptotically) optimal and is faster than DFS/BFS when answering more than a constant number of single-source queries. The data-structure uses at all times O(n) space. Our second contribution is a space-time tradeoff data-structure for distance queries. For any ϵ ∈ [1/2,1], we provide a data-structure with polynomial preprocessing time that allows pair queries in O(n 1-ϵ · α(n)) time, where α is the inverse of the Ackermann function, and at all times uses O(n ϵ) space. The input graph G is not considered in the space complexity.

Original languageUndefined/Unknown
Title of host publication24th Annual European Symposium on Algorithms (ESA 2016)
Place of publicationDagstuhl
PublisherSchloss Dagstuhl--Leibniz-Zentrum für Informatik
Publication date2016
Pages28:1-28:17
ISBN (Print)978-3-95977-015-6
DOIs
Publication statusPublished - 2016
SeriesLeibniz International Proceedings in Informatics
Volume57
ISSN1868-8969

Keywords

  • Constant-treewidth graphs
  • Distance queries
  • Graph algorithms
  • Reachability queries

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