The k-interchange-constrained diameter of a transit network: A connectedness indicator that accounts for travel convenience

TL;DR

This paper introduces a new connectivity indicator for transit networks based on a constrained shortest path problem, addressing limitations of traditional diameter metrics in capturing travel convenience.

Contribution

It proposes the k-interchange-constrained shortest path problem and demonstrates its effectiveness as a more accurate measure of network connectivity.

Findings

The k-interchange-constrained shortest path problem is tractable for certain k values.

Traditional diameter metrics do not adequately reflect travel convenience.

The new indicator improves network connectivity assessment.

Abstract

We study two variants of the shortest path problem. Given an integer k, the k-color-constrained and the k-interchange-constrained shortest path problems, respectively seek a shortest path that uses no more than k colors and one that makes no more than k - 1 alternations of colors. We show that the former problem is NP-hard, when the latter is tractable. The study of these problems is motivated by some limitations in the use of diameter-based metrics to evaluate the topological structure of transit networks. We notably show that indicators such as the diameter or directness of a transit network fail to adequately account for travel convenience in measuring the connectivity of a network and propose a new network indicator, based on solving the k-interchange-constrained shortest path problem, that aims at alleviating these limitations.