Improving Time Bounds on Maximum Generalised Flow Computations by Contracting the Network

Authors:
Tomasz Radzik
Affiliations:
-
Venue:
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Year:
2002

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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 脮(m2n log B) bound on the running time of the resulting algorithm. The previous best time bounds on computing maximum generalised flows were the O(m1.5n2 log B) bound of Kapoor and Vaidya's algorithm based on the interior-point method, and the 脮(m3 log B) bound of Goldfarb, Jin and Orlin's algorithm.