Layered Augmenting Path Algorithms

Augmenting path algorithms, first introduced by Ford and Fulkerson Ford, L. R., D. R. Fulkerson. 1962. Flows in Networks. Princeton University Press, Princeton, N.J., are widely used in optimization. Examples include Schonsleben's polymatroid intersection algorithm Schonsleben, P. 1980. Ganzzahlige polymatroid-intersection-algorithmen. Ph.D. thesis, Eidgenossischen Technischen Hochschule, Zurich., the maximum polymatroidal network flow algorithm of Lawler and Martel Lawler, E. L., C. U. Martel. 1982. Computing maximal polymatroidal network flows. Math. Oper. Res.7 334--347., Frank's algorithm for the Edmonds--Giles polyhedron Frank, A. 1984. Finding feasible vectors of Edmonds-Giles polyhedra. J. Combin. Theory Ser. B36 221-239. and Cunningham's algorithm for testing membership in matroid polyhedra Cunningham, H. W. 1984. Testing membership in matroid polyhedra. J. Combin. Theory Ser. B36 161--188.. Here we give an order of magnitude improvement for the above algorithms by using an approach analogous to that of Dinits' maximum flow algorithm Dinits, E. A. 1970. Algorithm for solution of a problem of maximum flow in a network with power estimation. Soviet Math. Dokl.11 1277--1280..