An optimal dual fault tolerant reachability oracle

Keerti Choudhary*

*Corresponding author for this work

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


Let G = (V,E) be an n-vertices m-edges directed graph. Let s 2 V be any designated source vertex. We address the problem of reporting the reachability information from s under two vertex failures. We show that it is possible to compute in polynomial time an O(n) size data structure that for any query vertex v, and any pair of failed vertices f1, f2, answers in O(1) time whether or not there exists a path from s to v in G \ {f1, f2}. For the simpler case of single vertex failure such a data structure can be obtained using the dominator-tree from the celebrated work of Lengauer and Tarjan [TOPLAS 1979, Vol. 1]. However, no efficient data structure was known in the past for handling more than one failures. We, in addition, also present a labeling scheme with O(log3 n)-bit size labels such that for any f1, f2, v 2 V , it is possible to determine in poly-logarithmic time if v is reachable from s in G \ {f1, f2} using only the labels of f1, f2 and v. Our data structure can also be seen as an efficient mechanism for verifying double-dominators. For any given x, y, v 2 V we can determine in O(1) time if the pair (x, y) is a double-dominator of v. Earlier the best known method for this problem was using dominator chain from which verification of double-dominators of only a single vertex was possible.

Original languageEnglish
Title of host publication43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016
EditorsYuval Rabani, Ioannis Chatzigiannakis, Davide Sangiorgi, Michael Mitzenmacher
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770132
StatePublished - 1 Aug 2016
Externally publishedYes
Event43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016 - Rome, Italy
Duration: 12 Jul 201615 Jul 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016


  • Directed graph
  • Fault tolerant
  • Labeling scheme
  • Reachability oracle


Dive into the research topics of 'An optimal dual fault tolerant reachability oracle'. Together they form a unique fingerprint.

Cite this