Multiple-Source Multiple-Sink Maximum Flow in Directed Planar Graphs in $O(n^{1.5} \log n)$ Time

Abstract

We give an $O(n^{1.5} \log n)$ algorithm that, given a directed planar graph with arc capacities, a set of source nodes and a set of sink nodes, finds a maximum flow from the sources to the sinks.Comment: to be merged with 1) Yahav Nussbaum 1012.4767 2) Philip N. Klein and Shay Mozes 1008.5332 3) Glencora Borradaile and Christian Wulff-Nilsen 1008.496