A Fixed-Parameter Linear-Time Algorithm to Compute Principal Typings of Planar Flow Networks

TL;DR

This paper introduces a simplified fixed-parameter linear-time algorithm for computing principal typings specifically for planar flow networks, leveraging the edge-outerplanarity parameter of the underlying graph.

Contribution

It presents a novel, simpler method that efficiently computes principal typings for planar flow networks in fixed-parameter linear time.

Findings

Algorithm runs in fixed-parameter linear-time for planar networks.

Method is simpler than previous approaches.

Performance depends on the edge-outerplanarity parameter.

Abstract

We present an alternative and simpler method for computing principal typings of flow networks. When limited to planar flow networks, the method can be made to run in fixed-parameter linear-time -- where the parameter not to be exceeded is what is called the edge-outerplanarity of the networks' underlying graphs.