A 1989 paper by Jerrum and Sinclair reduces a problem about finding these things to ferromagnetic instances of the Ising model to show that finding the partition function of the latter is #P-complete. A poly-time approximation ratio of 0.878 achieved by the Goemans-Williamson algorithm for a problem about these things is optimal only if the unique game conjecture holds. The size of one type of these things is equal to the total number of disjoint paths by Menger’s theorem. The Stoer-Wagner algorithm finds one of these things for (*) undirected graphs recursively, while Karger’s algorithm computes it probabilistically. The “minimum” one of these things can be produced from the Ford-Fulkerson algorithm via a namesake theorem that relates it to the maximum flow. For 10 points, name these partitions of a graph into two disjoint subsets of vertices. ■END■
ANSWER: graph cuts [or graph partitions until read; accept separating set; accept max(imum) cut; accept min(imum) cut; accept s-t cut; accept max-flow-min-cut]
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