New algorithms for the intersection problem of submodular systems

We consider the problem of finding a maximum common subbase of two submodular systems onE with |E|=n. First, we present a new algorithm by finding the shortest augmenting paths, which begins with a pair of subbases of the given submodular systems and is convenient for adopting the preflow-push approach of Goldberg and Tarjan. Secondly, by using the basic ideas of the preflow-push method, we devise a faster algorithm for the intersection problem, which requiresO(n3) push andO(n2) relabeling operations in total by the largest-label implementation with a specific order on the arc list of each vertex in the auxiliary graph.