Multicommodity flows in planar undirected graphs and shortest paths

Authors:
H Suzuki;T Nishizeki;N Saito
Affiliations:
Department of Electrical Communications, Faculty of Engineering, Tohoku University, Sendai, 980 Japan;Department of Electrical Communications, Faculty of Engineering, Tohoku University, Sendai, 980 Japan;Department of Electrical Communications, Faculty of Engineering, Tohoku University, Sendai, 980 Japan
Venue:
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Year:
1985

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Abstract

This paper deals with the multicommodity flow problems for two classes of planar undirected graphs. The first class C12 consists of graphs in which each source-sink pair is located on one of two specified face boundaries. The second class C01 consists of graphs in which some of the source-sink pairs are located on a specified face boundary and all the other pairs share a common sink located on the boundary. We show that the multicommodity flow problem for a graph in C12 (resp. C01) can be reduced to the shortest path problem for an undirected (resp. a directed) graph obtained from the dual of the original undirected graph.