Planar Network Diversion

TL;DR

This paper introduces a fast O(n log n) algorithm for the Network Diversion problem on planar graphs, significantly improving computational efficiency and enabling practical solutions for large transportation networks.

Contribution

It presents a novel, efficient algorithm for Network Diversion on planar graphs, supported by a practical implementation capable of handling large-scale instances.

Findings

Algorithm runs in O(n log n) time

Capable of solving large instances with millions of vertices

Demonstrates practical efficiency in transportation network analysis

Abstract

Network Diversion is a graph problem that has been extensively studied in both the network-analysis and operations-research communities as a measure of how robust a network is against adversarial disruption. This problem is especially well motivated in transportation networks, which are often assumed to be planar. Motivated by this and recent theoretical advances for Network Diversion on planar input graphs, we develop a fast O(n log n) time algorithm and present a practical implementation of this algorithm that is able to solve instances with millions of vertices in a matter of seconds.