Efficient algorithms for simplifying flow networks

Authors:
Ewa Misiołek;Danny Z. Chen
Affiliations:
Mathematics Department, Saint Mary’s College, Notre Dame, IN;Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN
Venue:
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Year:
2005

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Abstract

Computing flows in a network is a fundamental graph theory problem with numerous applications. In this paper, we present two algorithms for simplifying a flow network G=(V,E), i.e., detecting and removing from G all edges (and vertices) that have no impact on any source-to-sink flow in G. Such network simplification can reduce the size of the network and hence the amount of computation performed by maximum flow algorithms. For the undirected network case, we present the first linear time algorithm. For the directed network case, we present an O(|E|*(|V|+|E|)) time algorithm, an improvement over the previous best O(|V|+|E|2 log |V|) time solution. Both of our algorithms are quite simple.