Abstract
For an edge-weighted graph G with n vertices and m edges, we present a new deterministic algorithm for computing a minimum k-way cut for k=3,4. The algorithm runs in O(n k-1 F(n,m))=O(mn k log(n 2 /m)) time and O(n 2) space for k=3,4, where F(n,m) denotes the time bound required to solve the maximum flow problem in G. The bound for k=3 matches the current best deterministic bound O(mn 3) for weighted graphs, but improves the bound O(mn 3) to O(n 2 F(n,m))=O(min{mn 8/3,m 3/2 n 2}) for unweighted graphs. The bound O(mn 4) for k=4 improves the previous best randomized bound O(n 6) (for m=o(n 2)). The algorithm is then generalized to the problem of finding a minimum 3-way cut in a symmetric submodular system.
Published Version
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