Computing All Shortest Passenger Routes with a Tropical Dijkstra Algorithm

TL;DR

This paper introduces a novel tropical Dijkstra algorithm that efficiently computes all shortest passenger routes considering all possible timetables in public transportation networks.

Contribution

It presents a new polynomial-based Dijkstra algorithm over the tropical semiring for finding all efficient passenger routes in public transit networks.

Findings

Algorithm is computationally feasible on real-world networks

Successfully applied to Wuppertal public transport network

Effective in generating complete sets of shortest routes

Abstract

Given a public transportation network, which and how many passenger routes can potentially be shortest paths, when all possible timetables are taken into account? This question leads to shortest path problems on graphs with interval costs on their arcs and is closely linked to multi-objective optimization. We introduce a Dijkstra algorithm based on polynomials over the tropical semiring that computes complete or minimal sets of efficient paths. We demonstrate that this approach is computationally feasible by employing it on the public transport network of the city of Wuppertal and instances of the benchmarking set TimPassLib, and we evaluate the resulting sets of passenger routes.