An Efficient Algorithm for Computing Network Reliability in Small Treewidth

TL;DR

This paper introduces a simple, efficient fixed-parameter algorithm for computing network reliability in graphs with small treewidth, demonstrating its practicality on real-world transit network data.

Contribution

It presents the first scalable, exact algorithm for network reliability in real-world graphs with small treewidth, simplifying previous complex methods.

Findings

Algorithm runs in linear time for fixed treewidth

Successfully applied to subway and transit networks of major cities

First exact scalable solution for real-world network reliability

Abstract

We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated probability and the problem is to determine the probability of having at least one source-to-target path. This problem is known to be NP-hard. We present a linear-time fixed-parameter algorithm based on a parameter called treewidth, which is a measure of tree-likeness of graphs. Network Reliability was already known to be solvable in polynomial time for bounded treewidth, but there were no concrete algorithms and the known methods used complicated structures and were not easy to implement. We provide a significantly simpler and more intuitive algorithm that is much easier to implement. We also report on an implementation of our algorithm and establish the applicability of our approach by providing experimental results on the graphs of subway and transit systems of several major cities, such as London and Tokyo. To the best of our knowledge, this is the first exact algorithm for Network Reliability that can scale to handle real-world instances of the problem.