Approximation algorithms for minimum-cost k-vertex connected subgraphs

Authors:
Joseph Cheriyan;Santosh Vempala;Adrian Vetta
Affiliations:
University of Waterloo;Massachusetts Institute of Technology;Massachusetts Institute of Technology
Venue:
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Year:
2002

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Abstract

(MATH) We present two new algorithms for the problem of finding a minimum-cost k-vertex connected spanning subgraph. The first algorithm works on undirected graphs with at least 6k2 vertices and achieves an approximation factor of 6 times the kth harmonic number, which is $O(\log k)$. The second algorithm works on directed and undirected graphs. It gives an $O(\sqrt{ n /\keps})$-approximation algorithm for any $\keps 0$ and $k \le (1-\keps)n$. 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).