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

TL;DR

This paper introduces an efficient algorithm for computing maximum flow in directed planar graphs with multiple sources and sinks, achieving a time complexity of O(n^{1.5} log n).

Contribution

The paper presents the first algorithm with O(n^{1.5} log n) time complexity for multiple-source, multiple-sink maximum flow in directed planar graphs.

Findings

Achieves maximum flow in directed planar graphs with multiple sources and sinks.

Runs in O(n^{1.5} log n) time, improving previous algorithms.

Applicable to large-scale planar network flow problems.

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.