An Efficient Algorithm for Finding Multicommodity Flows in Planar Networks

Abstract

This paper presents an efficient algorithm for finding multicommodity flows in planar graphs. Suppose that G is an undirected planar graph with all sources and sinks on the boundary of the outer face and that a real-valued demand is given for each source–sink pair. The algorithm decides whether G has multicommodity flows, each from a source to a sink and of a given demand, and actually finds them if G has. It spends $O(kn + n^2 (\log n)^{1/2} )$ time and $O(kn)$ space if G has n vertices and k source–sink pairs.