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Algorithms for Finding Shortest Paths in Networks with Vertex Transfer Penalties

School of Mathematics, Cardiff University, Cardiff CF10 3AT, Wales, UK
Algorithms 2020, 13(11), 269; https://doi.org/10.3390/a13110269
Received: 29 September 2020 / Revised: 15 October 2020 / Accepted: 18 October 2020 / Published: 22 October 2020
(This article belongs to the Special Issue Algorithms for Graphs and Networks)
In this paper we review many of the well-known algorithms for solving the shortest path problem in edge-weighted graphs. We then focus on a variant of this problem in which additional penalties are incurred at the vertices. These penalties can be used to model things like waiting times at road junctions and delays due to transfers in public transport. The usual way of handling such penalties is through graph expansion. As an alternative, we propose two variants of Dijkstra’s algorithm that operate on the original, unexpanded graph. Analyses are then presented to gauge the relative advantages and disadvantages of these methods. Asymptotically, compared to using Dijkstra’s algorithm on expanded graphs, our first variant is faster for very sparse graphs but slower with dense graphs. In contrast, the second variant features identical worst-case run times. View Full-Text
Keywords: shortest path problems; Dijkstra’s algorithm; transfer penalties; public transport shortest path problems; Dijkstra’s algorithm; transfer penalties; public transport
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Lewis, R. Algorithms for Finding Shortest Paths in Networks with Vertex Transfer Penalties. Algorithms 2020, 13, 269.

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