Abstract
We consider the maximum generalised network flow problem and a supply-scaling algorithmic framework for this problem. We present three network-modification operations, which may significantly decrease the size of the network when the remaining node supplies become small. We use these three operations in Goldfarb, Jin and Orlin’s supply-scaling algorithm and prove a Õ(m 2 n log B) bound on the running time of the resulting algorithm. The previous best time bounds on computing maximum generalised flows were the O(m 1.5 n 2 log B) bound of Kapoor and Vaidya’s algorithm based on the interior-point method, and the Õ(m 3 log B) bound of Goldfarb, Jin and Orlin’s algorithm.
This work was supported by the UK EPSRC grant GR/L81468.
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Radzik, T. (2002). Improving Time Bounds on Maximum Generalised Flow Computations by Contracting the Network. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_52
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DOI: https://doi.org/10.1007/3-540-45465-9_52
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