Boundary-to-boundary flows in planar graphs

TL;DR

This paper presents an efficient iterative algorithm for computing maximum flows between boundary sources and sinks in planar graphs, using simple data structures and achieving an optimal O(n log n) runtime.

Contribution

It introduces a practical, simple-primitive-based algorithm that improves upon previous divide-and-conquer methods for boundary-to-boundary flows in planar graphs.

Findings

Achieves O(n log n) running time for maximum flow computation

Uses only O(n) queries to simple data structures

Simplifies previous algorithms by avoiding complex shortest-path computations

Abstract

We give an iterative algorithm for finding the maximum flow between a set of sources and sinks that lie on the boundary of a planar graph. Our algorithm uses only O(n) queries to simple data structures, achieving an O(n log n) running time that we expect to be practical given the use of simple primitives. The only existing algorithm for this problem uses divide and conquer and, in order to achieve an O(n log n) running time, requires the use of the (complicated) linear-time shortest-paths algorithm for planar graphs.