We explore balancing as a definitional and algorithmic tool for finding minimum cuts and maximum flows in ordinary and parametric networks. We show that a standard monotonic parametric maximum flow problem can be formulated as a problem of computing a particular maximum flow that is balanced in an appropriate sense. We present a divide-and-conquer algorithm to compute such a balanced flow in a logarithmic number of ordinary maximum-flow computations. For the special case of a bipartite network, we present two simple, local algorithms for computing a balanced flow. The local balancing idea becomes even simpler when applied to the ordinary maximum flow problem. For this problem, we present a round-robin arc-balancing algorithm that computes a maximum flow on an n-vertex, m-arc network with integer arc capacities of at most U in O(n 2m log(nU)) time. Although this algorithm is slower by at least a factor of n than other known algorithms, it is extremely simple and well-suited to parallel and distributed implementation. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Tarjan, R., Ward, J., Zhang, B., Zhou, Y., & Mao, J. (2006). Balancing applied to maximum network flow problems (extended abstract). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4168 LNCS, pp. 612–623). Springer Verlag. https://doi.org/10.1007/11841036_55
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