The connectivity carcass of a vertex subset in a graph and its incremental maintenance

Y. E. Dinitz, A. Vainshteint

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

12 Scopus citations

Abstract

Let G = (V, E) be an undirected graph, S be a subset of its vertices, ts be the set of minimum edge-cuts partitioning S. A data structure representing both cuts in I.Z,S and the partition of V by all these cuts is suggested. One can build it in ISI - 1 max-flow computations in G. It can be maintained, for an arbitrary sequence of u edge insertions, in O(min{]V]. Il?l, klV12 +wa(u, IVI)}) time, where k is the size of a cut in C.g. For two vertices of G, queries asking whether they are separated by a cut in C.S are answered in O (a (q, IV t) ) amortized time per query, where q is the number of queries; such a cut itself is shown in O ( IVI ) amortized time. The dag representation of all cuts in C,S separating two given vertices in S is obtained in O(min{lEl, klVl}) amortized time.

Original languageEnglish
Title of host publicationProceedings of the 26th Annual ACM Symposium on Theory of Computing, STOC 1994
PublisherAssociation for Computing Machinery
Pages716-725
Number of pages10
ISBN (Electronic)0897916638
DOIs
StatePublished - 23 May 1994
Externally publishedYes
Event26th Annual ACM Symposium on Theory of Computing, STOC 1994 - Montreal, Canada
Duration: 23 May 199425 May 1994

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
VolumePart F129502
ISSN (Print)0737-8017

Conference

Conference26th Annual ACM Symposium on Theory of Computing, STOC 1994
Country/TerritoryCanada
CityMontreal
Period23/05/9425/05/94

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