A simple algorithm that proves half-integrality of bidirected network programming

In a bidirected graph, each end of each edge is independently oriented. We show how to express any column of the incidence matrix as a half-integral linear combination of any column basis, through a simplification, based on an idea of Bolker, of a combinatorial algorithm of Appa and Kotnyek. Corollaries are that the inverse of each nonsingular square submatrix has entries 0, ±12 , and ±1, and that a bidirected integral linear program has half-integral solutions. Mathematics Subject Classifications (2000). Primary 05C22, Secondary 05B35, 05C20, 90C10.