Limited Maximum Flow Problem With Multiple Sink Vertices

Ruijie He

Keywords: graph theory, network flow, directed acyclic graph, linear basis, hash

Abstract: We propose a stochastic algorithm for limited maximum flow problem with multiple sink vertices in directed acyclic graph, which is completely different from the traditional network flow algorithms. The algorithm shows significant performance advantages when computing the maximum flow for all vertices. Compared to the Dinic algorithm solution with complexity $O(nm^{\frac 3 2})$, our algorithm can optimize the complexity to $O(mk^2)$ with considerable theoretical correctness. In practice, its performance and correctness are better than the currently known bounds.

Submission Number: 28