A fast algorithm for computing Steiner edge connectivity

Richard Cole, Ramesh Hariharan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Given an undirected graph or an Eulerian directed graph G and a subset S of its vertices, we show how to determine the edge connectivity C of the vertices in S in time O(C3n logn + m). This algorithm is based on an efficient construction of tree packings which generalizes Edmonds' Theorem. These packings also yield a characterization of all minimal Steiner cuts of size C from which an efficient data structure for maintaining edge connectivity between vertices in S under edge insertion can be obtained. This data structure enables the efficient construction of a cactus tree for representing significant C-cuts among these vertices, called C-separations, in the same time bound. In turn, we use the cactus tree to give a fast implementation of an approximation algorithm for the Survivable Network Design problem due to Williamson, Goemans, Mihail and Vazirani.

Original languageEnglish (US)
Title of host publicationConference Proceedings of the Annual ACM Symposium on Theory of Computing
Pages167-176
Number of pages10
StatePublished - 2003
Event35th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States
Duration: Jun 9 2003Jun 11 2003

Other

Other35th Annual ACM Symposium on Theory of Computing
CountryUnited States
CitySan Diego, CA
Period6/9/036/11/03

Fingerprint

Data structures
Directed graphs
Approximation algorithms

Keywords

  • Cactus trees
  • Edge-connectivity
  • Steiner points

ASJC Scopus subject areas

  • Software

Cite this

Cole, R., & Hariharan, R. (2003). A fast algorithm for computing Steiner edge connectivity. In Conference Proceedings of the Annual ACM Symposium on Theory of Computing (pp. 167-176)

A fast algorithm for computing Steiner edge connectivity. / Cole, Richard; Hariharan, Ramesh.

Conference Proceedings of the Annual ACM Symposium on Theory of Computing. 2003. p. 167-176.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Cole, R & Hariharan, R 2003, A fast algorithm for computing Steiner edge connectivity. in Conference Proceedings of the Annual ACM Symposium on Theory of Computing. pp. 167-176, 35th Annual ACM Symposium on Theory of Computing, San Diego, CA, United States, 6/9/03.
Cole R, Hariharan R. A fast algorithm for computing Steiner edge connectivity. In Conference Proceedings of the Annual ACM Symposium on Theory of Computing. 2003. p. 167-176
Cole, Richard ; Hariharan, Ramesh. / A fast algorithm for computing Steiner edge connectivity. Conference Proceedings of the Annual ACM Symposium on Theory of Computing. 2003. pp. 167-176
@inproceedings{5aef1f17bdc641509a7ef07065db8fc7,
title = "A fast algorithm for computing Steiner edge connectivity",
abstract = "Given an undirected graph or an Eulerian directed graph G and a subset S of its vertices, we show how to determine the edge connectivity C of the vertices in S in time O(C3n logn + m). This algorithm is based on an efficient construction of tree packings which generalizes Edmonds' Theorem. These packings also yield a characterization of all minimal Steiner cuts of size C from which an efficient data structure for maintaining edge connectivity between vertices in S under edge insertion can be obtained. This data structure enables the efficient construction of a cactus tree for representing significant C-cuts among these vertices, called C-separations, in the same time bound. In turn, we use the cactus tree to give a fast implementation of an approximation algorithm for the Survivable Network Design problem due to Williamson, Goemans, Mihail and Vazirani.",
keywords = "Cactus trees, Edge-connectivity, Steiner points",
author = "Richard Cole and Ramesh Hariharan",
year = "2003",
language = "English (US)",
pages = "167--176",
booktitle = "Conference Proceedings of the Annual ACM Symposium on Theory of Computing",

}

TY - GEN

T1 - A fast algorithm for computing Steiner edge connectivity

AU - Cole, Richard

AU - Hariharan, Ramesh

PY - 2003

Y1 - 2003

N2 - Given an undirected graph or an Eulerian directed graph G and a subset S of its vertices, we show how to determine the edge connectivity C of the vertices in S in time O(C3n logn + m). This algorithm is based on an efficient construction of tree packings which generalizes Edmonds' Theorem. These packings also yield a characterization of all minimal Steiner cuts of size C from which an efficient data structure for maintaining edge connectivity between vertices in S under edge insertion can be obtained. This data structure enables the efficient construction of a cactus tree for representing significant C-cuts among these vertices, called C-separations, in the same time bound. In turn, we use the cactus tree to give a fast implementation of an approximation algorithm for the Survivable Network Design problem due to Williamson, Goemans, Mihail and Vazirani.

AB - Given an undirected graph or an Eulerian directed graph G and a subset S of its vertices, we show how to determine the edge connectivity C of the vertices in S in time O(C3n logn + m). This algorithm is based on an efficient construction of tree packings which generalizes Edmonds' Theorem. These packings also yield a characterization of all minimal Steiner cuts of size C from which an efficient data structure for maintaining edge connectivity between vertices in S under edge insertion can be obtained. This data structure enables the efficient construction of a cactus tree for representing significant C-cuts among these vertices, called C-separations, in the same time bound. In turn, we use the cactus tree to give a fast implementation of an approximation algorithm for the Survivable Network Design problem due to Williamson, Goemans, Mihail and Vazirani.

KW - Cactus trees

KW - Edge-connectivity

KW - Steiner points

UR - http://www.scopus.com/inward/record.url?scp=0038107722&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038107722&partnerID=8YFLogxK

M3 - Conference contribution

SP - 167

EP - 176

BT - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

ER -