## A polylogarithmic approximation algorithm for the group Steiner tree problem (2000)

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Venue: | Journal of Algorithms |

Citations: | 130 - 9 self |

### BibTeX

@INPROCEEDINGS{Garg00apolylogarithmic,

author = {Naveen Garg and Goran Konjevod and R. Ravi},

title = {A polylogarithmic approximation algorithm for the group Steiner tree problem},

booktitle = {Journal of Algorithms},

year = {2000},

pages = {253--259}

}

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### Abstract

The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimum-weight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich and Widmayer and finds applications in VLSI design. The group Steiner tree problem generalizes the set covering problem, and is therefore at least as had. We give a randomized O(log 3 n log k)-approximation algorithm for the group Steiner tree problem on an n-node graph, where k is the number of groups. The best previous ink)v/ (Bateman, Helvig, performance guarantee was (1 + - Robins and Zelikovsky).