Multiple-source single-sink maximum flow in directed planar graphs in $O(n^{1.5} \log n)$ time

TL;DR

This paper presents the first subquadratic-time strongly polynomial algorithm for computing maximum flow from multiple sources to a single sink in directed planar graphs, significantly improving efficiency.

Contribution

It introduces an $O(n^{1.5} ext{log} n)$ algorithm for maximum flow in directed planar graphs with multiple sources and one sink, a novel advancement in the field.

Findings

Achieves $O(n^{1.5} ext{log} n)$ time complexity

First subquadratic algorithm for this problem

Strongly polynomial algorithm with practical efficiency

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 single sink node, finds a maximum flow from the sources to the sink . This is the first subquadratic-time strongly polynomial algorithm for the problem.