A combinatorial algorithm for minimizing symmetric submodular functions

We describe a purely combinatorial algorithm which, given a submodular set function f on a finite set V, finds a proper subset A of V minimizing f[A]+f[V\A]. This algorithm, an extension of the Nagamochi-Ibaraki minimum cut algorithm as simplified by Stoer and Wagner (1994) and by F’rank (1994), minimizes any symmetric submodular function using O(lVl”) calls to a function value oracle.