Quick Max-flow Algorithm

Abstract

Determining of a maximal network flow is a classic problem in discrete optimization with many applications. In this paper, a new algorithm based on the Dinic’s method is presented. Algorithms of the Dinic’s method work evidently faster than theoretical bounds for a randomized network. This paper presents a parameterized and easy to implement family of algorithms of finding a saturating flow in a layered network. Although their common complexity is poor O(V2L) where L is the number of layers, three particular members are proved to be O(V2). Furthermore, there is a particularly interesting “balanced” member of the family for which a calculated upper bound on complexity is still O(V2L) but there is known no example of a layered network that needs more than O(E + V(3/2)) time to resolve. All the considered members work really quickly for randomized examples of a layered network. Starting from the above family, three algorithms which find maximal flow in a network in O(V3) worst case time have been constructed, while the respective “balanced” algorithm is theoretically O(V4). All the algorithms do not extend O(V2) time in experimental, i.e. randomized, cases.