Fault tolerant reachability for directed graphs

Surender Baswana, Keerti Choudhary*, Liam Roditty

*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 ∈ 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
Number of pages16
ISBN (Print)9783662486528
StatePublished - 2015
Externally publishedYes
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)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference29th International Symposium on Distributed Computing, DISC 2015


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