1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2: Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3: The Classical Sequent Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

We show that the following two problems are polynomiaUy equivalent: 1) Given a (weighted) graph G, and a cut C of G, decide whether C is maximal or not . 2) Given a (weighted) graph G, and a cut C of G, decide whether C is maximal or not , and in case it is not , find a better solution C'. As a consequence, an optimali ty testing oracle may be used to design a polynomial t ime algori thm for ap...

We give query-efficient algorithms for the global min-cut and the s-t cut problem in unweighted, undirected graphs. Our oracle model is inspired by the submodular function minimization problem: on query S ⊂ V , the oracle returns the size of the cut between S and V \ S. We provide algorithms computing an exact minimum s-t cut in G with Õ(n5/3) queries, and computing an exact global minimum cut ...