Abstract
We present an algebraic approach for computing the distribution of the capacity of a minimum s-t cut in a network, in which the arc capacities have known (discrete) probability distributions. Algorithms are developed to determine the exact distribution as well as upper and lower bounding distributions on the capacity of a minimum cut. This approach then provides exact and bounding distributions on the maximum flow in such stochastic networks. We also obtain bounds on the expected capacity of a minimum cut (and the expected maximum flow value).
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Hastings, K.C., Shier, D.R. (2011). Algebraic Methods for Stochastic Minimum Cut and Maximum Flow Problems. In: Pahl, J., Reiners, T., Voß, S. (eds) Network Optimization. INOC 2011. Lecture Notes in Computer Science, vol 6701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21527-8_35
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DOI: https://doi.org/10.1007/978-3-642-21527-8_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21526-1
Online ISBN: 978-3-642-21527-8
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