After [10, 15, 12, 2, 4] minimum cut/maximum ow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-ow algorithms with dierent polynomial time complexity. Their practical eciency, however, has to date been studied mainly outside the scope of computer vision.

The maximum integer skew-symmetric ow problem (MSFP) generalizes both the maximum ow and maximum matching problems. It was introduced by Tutte [28] in terms of self-conjugate ows in antisymmetrical digraphs. He showed that for these objects there are natural analogs of classical theoretical results on usual network ows, such as the ow decomposition, augmenting path, and max-ow min-cut theorems. We review those theoretical results and give uni ed and relatively short proofs for them.

B = ; Definition 3 The capacity of a cut, cap(A; B) = P u2A;v2B c(u; v) Definition 4 The value of the ow in the graph is dened as f = P (u;v)2E f(u; v). The ow across a cut (A; B) is depicted in gure 1 where the solid arrows represent the edges that are counted in a minimum cut and the dashed edges indicate back edges from B to A that are not counted. Observation 1 For any s-t cut (A; B) and ow f , f = P (u;v):u2A;v2B f(u; v) Observation 2 The value of