TY - GEN

T1 - The connectivity carcass of a vertex subset in a graph and its incremental maintenance

AU - Dinitz, Y. E.

AU - Vainshteint, A.

N1 - Funding Information:
1This research was supported by Research at the Technion, Israel. ‘2up to IWO: E. A. Dinic, MOSCOW.
Publisher Copyright:
© 1994 ACM.

PY - 1994/5/23

Y1 - 1994/5/23

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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0028062303&partnerID=8YFLogxK

U2 - 10.1145/195058.195442

DO - 10.1145/195058.195442

M3 - Conference contribution

AN - SCOPUS:0028062303

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 716

EP - 725

BT - Proceedings of the 26th Annual ACM Symposium on Theory of Computing, STOC 1994

PB - Association for Computing Machinery

T2 - 26th Annual ACM Symposium on Theory of Computing, STOC 1994

Y2 - 23 May 1994 through 25 May 1994

ER -