### 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(C^{3}n 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 language | English (US) |
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Title of host publication | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

Pages | 167-176 |

Number of pages | 10 |

State | Published - 2003 |

Event | 35th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States Duration: Jun 9 2003 → Jun 11 2003 |

### Other

Other | 35th Annual ACM Symposium on Theory of Computing |
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Country | United States |

City | San Diego, CA |

Period | 6/9/03 → 6/11/03 |

### Fingerprint

### Keywords

- Cactus trees
- Edge-connectivity
- Steiner points

### ASJC Scopus subject areas

- Software

### Cite this

*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.

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

*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.

}

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

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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 -