Multiple source, single sink maximum flow in a planar graph

TL;DR

This paper presents an efficient algorithm for computing maximum flow in directed planar graphs with multiple sources and a single sink, extending to bounded genus graphs with improved time complexity.

Contribution

It introduces an $O(n^{1.5} ext{log} n)$ time algorithm for maximum flow in such graphs, generalizing previous methods to bounded genus graphs.

Findings

Achieves $O(n^{1.5} ext{log} n)$ time complexity for planar graphs.

Extends techniques to bounded genus graphs with subquadratic time.

Provides a new approach for multiple source, single sink maximum flow problems.

Abstract

We give an $O(n^{1.5}\log n)$ time algorithm for finding the maximum flow in a directed planar graph with multiple sources and a single sink. The techniques generalize to a subquadratic time algorithm for bounded genus graphs.