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(V 2 L) where L is the number of layers, three particular members are proved to be O(V 2). Furthermore, there is a particularly interesting “balanced” member of the family for which a calculated upper bound on complexity is still O(V 2 L) 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(V 3) worst case time have been constructed, while the respective “balanced” algorithm is theoretically O(V 4). All the algorithms do not extend O(V 2) time in experimental, i.e. randomized, cases.
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Gordinowicz, P. Quick Max-flow Algorithm. J Math Model Algor 8, 19–34 (2009). https://doi.org/10.1007/s10852-008-9091-z
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DOI: https://doi.org/10.1007/s10852-008-9091-z