A new Karzanov-type O(n3) max-flow algorithm

Abstract

A new algorithm is presented for finding maximal and maximum value flows in directed single commodity networks. The algorithm gradually converts a combination of blocking preflows and backflows to a maximal flow in the network. Unlike other maximal flow algorithms, the algorithm treats the network more symmetrically by attempting to increase flow on both the ForwardStep and the BackwardStep. The algorithm belongs to the so called phase algorithms, and is applied to Dinic-type layered networks. With an effort of at most O(n3) for maximum value flow, the algorithm ties with the fastest maximum flow algorithms in dense networks, where m [approximate] n2, and can therefore be seen as a significant alternate technique. The algorithm is based on the Karzanov [1] algorithm, and shares features with the algorithm of Tarjan [2]. The first version of this algorithm was presented by the author in [3].