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Approximation Algorithms for Minimum-Cost k-Vertex Connected Subgraphs (2002)
| Venue: | In 34th Annual ACM Symposium on the Theory of Computing |
| Citations: | 68 - 2 self |
BibTeX
@INPROCEEDINGS{Cheriyan02approximationalgorithms,
author = {Joseph Cheriyan and Santosh Vempala and Adrian Vetta},
title = {Approximation Algorithms for Minimum-Cost k-Vertex Connected Subgraphs},
booktitle = {In 34th Annual ACM Symposium on the Theory of Computing},
year = {2002},
pages = {306--312}
}
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Abstract
We present two new algorithms for the problem of nding a minimum-cost k-vertex connected spanning subgraph. The rst algorithm works on undirected graphs with at least 6k vertices and achieves an approximation of 6 times the kth harmonic number (which is O(log k)), The second algorithm works on any graph (directed or undirected) and gives an O( n=)-approximation algorithm for any > 0 and k (1 )n. These algorithms improve on the previous best approximation factor (more than k=2). The latter algorithm also extends to other problems in network design with vertex connectivity requirements. Our main tools are setpair relaxations, a theorem of Mader's (in the undirected case) and iterative rounding (general case).
Keyphrases
approximation algorithm minimum-cost k-vertex connected subgraphs kth harmonic number network design approximation factor undirected graph setpair relaxation rst algorithm work algorithm improve second algorithm work undirected case main tool latter algorithm vertex connectivity requirement general case minimum-cost k-vertex new algorithm iterative rounding
