When determining the paths of the passengers in public transport, the travel time is usually the main criterion. However, also the ticket price a passenger has to pay is a relevant factor for choosing the path. The ticket price is also relevant for simulating the minimum income a public transport company can expect. However, finding the correct price depends on the fare system used (e.g., distance tariff, zone tariff with different particularities, application of a short-distance tariff, etc.) and may be rather complicated even if the path is already fixed. An algorithm which finds a cheapest path in a very general case has been provided in [R. Euler and R. Borndörfer, 2019], but its running time is exponential. In this paper, we model and analyze different fare systems, identify important properties they may have and provide polynomial algorithms for computing a cheapest path.
@InProceedings{schobel_et_al:OASIcs.ATMOS.2020.13, author = {Sch\"{o}bel, Anita and Urban, Reena}, title = {{Cheapest Paths in Public Transport: Properties and Algorithms}}, booktitle = {20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020)}, pages = {13:1--13:16}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-170-2}, ISSN = {2190-6807}, year = {2020}, volume = {85}, editor = {Huisman, Dennis and Zaroliagis, Christos D.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2020.13}, URN = {urn:nbn:de:0030-drops-131499}, doi = {10.4230/OASIcs.ATMOS.2020.13}, annote = {Keywords: Public Transport, Fare Systems, Modeling, Cheapest Paths} }
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