@MISC{Nanongkai14almost-tightdistributed, author = {Danupon Nanongkai and et al.}, title = {Almost-Tight Distributed Minimum Cut Algorithms }, year = {2014} }

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Abstract

We study the problem of computing the minimum cut in a weighted distributed message-passing networks (the CONGEST model). Let λ be the minimum cut, n be the number of nodes (processors) in the network, and D be the network diameter. Our algorithm can compute λ exactly in O(( n log ∗ n+D)λ4 log2 n) time. To the best of our knowledge, this is the first paper that explicitly studies computing the exact minimum cut in the distributed setting. Previously, non-trivial sublinear time algorithms for this problem are known only for unweighted graphs when λ ≤ 3 due to Pritchard and Thurimella’s O(D)-time and O(D + n1/2 log ∗ n)-time algo-rithms for computing 2-edge-connected and 3-edge-connected components [ACM Transactions on Algorithms 2011]. By using the edge sampling technique of Karger [STOC 1994], we can convert this algorithm into a (1 + )-approximation O(( n log ∗ n + D)−5 log3 n)-time algorithm for any > 0. This improves over the previous (2 + )-approximation O((