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

Y. E. Dinitz; A. Vainshteint

doi:10.1145/195058.195442

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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 language	English
Title of host publication	Proceedings of the 26th Annual ACM Symposium on Theory of Computing, STOC 1994
Publisher	Association for Computing Machinery
Pages	716-725
Number of pages	10
ISBN (Electronic)	0897916638
DOIs	https://doi.org/10.1145/195058.195442
State	Published - 23 May 1994
Externally published	Yes
Event	26th Annual ACM Symposium on Theory of Computing, STOC 1994 - Montreal, Canada Duration: 23 May 1994 → 25 May 1994

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
Volume	Part F129502
ISSN (Print)	0737-8017

Conference

Conference	26th Annual ACM Symposium on Theory of Computing, STOC 1994
Country/Territory	Canada
City	Montreal
Period	23/05/94 → 25/05/94

Bibliographical note

Publisher Copyright:
© 1994 ACM.

ASJC Scopus subject areas

Software

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10.1145/195058.195442

Cite this

Dinitz, Y. E., & Vainshteint, A. (1994). The connectivity carcass of a vertex subset in a graph and its incremental maintenance. In Proceedings of the 26th Annual ACM Symposium on Theory of Computing, STOC 1994 (pp. 716-725). (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. Part F129502). Association for Computing Machinery. https://doi.org/10.1145/195058.195442

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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.",

author = "Dinitz, \{Y. E.\} and A. Vainshteint",

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year = "1994",

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doi = "10.1145/195058.195442",

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Dinitz, YE & Vainshteint, A 1994, The connectivity carcass of a vertex subset in a graph and its incremental maintenance. in Proceedings of the 26th Annual ACM Symposium on Theory of Computing, STOC 1994. Proceedings of the Annual ACM Symposium on Theory of Computing, vol. Part F129502, Association for Computing Machinery, pp. 716-725, 26th Annual ACM Symposium on Theory of Computing, STOC 1994, Montreal, Canada, 23/05/94. https://doi.org/10.1145/195058.195442

The connectivity carcass of a vertex subset in a graph and its incremental maintenance. / Dinitz, Y. E.; Vainshteint, A.
Proceedings of the 26th Annual ACM Symposium on Theory of Computing, STOC 1994. Association for Computing Machinery, 1994. p. 716-725 (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. Part F129502).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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.

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

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