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Date: 15-3-2022
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Let be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut of is any nontrivial subset of , and the weight of the cut is the sum of weights of edges crossing the cut. A mincut is then defined as a cut of of minimum weight. The problem is polynomial time solvable as a series of network flow problems or using the algorithm of Stoer and Wagner (1994).
Stoer, M. and Wagner, F. "A Simple Min Cut Algorithm." Algorithms--ESA '94, LNCS 855, 141-147, 1994.
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