An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm

Authors:
Yonatan Aumann;Yuval Rabani
Affiliations:
-;-
Venue:
SIAM Journal on Computing
Year:
1998

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Abstract

It is shown that the minimum cut ratio is within a factor of O(log k) of the maximum concurrent flow for k-commodity flow instances with arbitrary capacities and demands. This improves upon the previously best-known bound of O(log2 k) and is existentially tight, up to a constant factor. An algorithm for finding a cut with ratio within a factor of O(log k) of the maximum concurrent flow, and thus of the optimal min-cut ratio, is presented.