Fault tolerant reachability for directed graphs

Surender Baswana, Keerti Choudhary, Liam Roditty

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

15 Scopus citations

Abstract

Let G = (V,E) be an n-vertices m-edges directed graph. Let s ∈ V be any designated source vertex, and let T be an arbitrary reachability tree rooted at s. We address the problem of finding a set of edges ε ⊆ E\T of minimum size such that on a failure of any vertex w ∈ V, the set of vertices reachable from s in T ∪ ε\{w} is the same as the set of vertices reachable from s in G\{w}. We obtain the following results: • The optimal set ε for any arbitrary reachability tree T has at most n − 1 edges. • There exists an O(mlog n)-time algorithm that computes the optimal set ε for any given reachability tree T. For the restricted case when the reachability tree T is a Depth-First- Search (DFS) tree it is straightforward to bound the size of the optimal set ε by n − 1 using semidominators with respect to DFS trees from the celebrated work of Lengauer and Tarjan [13]. Such a set ε can be computed in O(m) time using the algorithm of Buchsbaum et. al [4]. To bound the size of the optimal set in the general case we define semidominators with respect to arbitrary trees. We also present a simple O(mlog n) time algorithm for computing such semidominators. As a byproduct, we get an alternative algorithm for computing dominators in O(mlog n) time.

Original languageEnglish
Title of host publicationDistributed Computing - 29th International Symposium, DISC 2015, Proceedings
EditorsYoram Moses
PublisherSpringer Verlag
Pages528-543
Number of pages16
ISBN (Print)9783662486528
DOIs
StatePublished - 2015
Event29th International Symposium on Distributed Computing, DISC 2015 - Tokyo, Japan
Duration: 7 Oct 20159 Oct 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9363
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference29th International Symposium on Distributed Computing, DISC 2015
Country/TerritoryJapan
CityTokyo
Period7/10/159/10/15

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

Funding

This research was partially supported by Israel Science Foundation (ISF) and University Grants Commission (UGC) of India. The research of the second author was partially supported by Google India under the Google India PhD Fellowship Award.

FundersFunder number
Google India
Israel Science Foundation
University Grants Commission
University Grants Commission
Israel Science Foundation

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