In this work, we investigate properties of the function taking the real value h to the max h-route flow value, and apply the result to solve robust network flow problems. We show that the function is piecewise hyperbolic, and modify a parametric optimization technique, the ES algorithm, to find this function. The running time of the algorithm is O(λmn), when λ is a source-sink edge connectivity of our network, m is the number of links, and n is the number of nodes. We can use the result from that algorithm to solve two max-flow problems against k edge failures, referred to as max-MLA-robust flow and max-MLA-reliable flow. When h is optimally chosen from the function, we show that the max-h-route flow is an exact solution of both problems for graphs in a specific class. Our numerical experiments show that of random graphs generated in the experiment are in that specific class. Given a parametric edge e, we also show that the function taking the capacity of e to the max-h-route flow value is linear piecewise. Hence we can apply our modified ES algorithm to find that function in O(h2mn). © 2014 Springer International Publishing.
CITATION STYLE
Baffier, J. F., Suppakitpaisarn, V., Hiraishi, H., & Imai, H. (2014). Parametric multiroute flow and its application to robust network with k edge failures. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8596 LNCS, pp. 26–37). Springer Verlag. https://doi.org/10.1007/978-3-319-09174-7_3
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