2026-07-22T22:34:18Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:11426 2024-03-06T10:30:48Z ddc:004 open_access

An Asymptotically Optimal Approximation Algorithm for the Travelling Car Renter Problem Pedrosa, Lehilton L. C. Quesquén, Greis Y. O. Schouery, Rafael C. S. Approximation Algorithm Travelling Car Renter Problem LP-rounding Separation Problem In the classical Travelling Salesman Problem (TSP), one wants to find a route that visits a set of n cities, such that the total travelled distance is minimum. An often considered generalization is the Travelling Car Renter Problem (CaRS), in which the route is travelled by renting a set of cars and the cost to travel between two given cities depends on the car that is used. The car renter may choose to swap vehicles at any city, but must pay a fee to return the car to its pickup location. This problem appears in logistics and urban transportation when the vehicles can be provided by multiple companies, such as in the tourism sector. In this paper, we consider the case in which the return fee is some fixed number g >= 0, which we call the Uniform CaRS (UCaRS). We show that, already for this version, there is no o(log n)-approximation algorithm unless P = NP. The main contribution is an O(log n)-approximation algorithm for the problem, which is based on the randomized rounding of an exponentially large LP-relaxation. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Lehilton L. C. Pedrosa and Greis Y. O. Quesquén and Rafael C. S. Schouery 2019 Is Part Of OASIcs, Volume 75, 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/OASIcs.ATMOS.2019.14 urn:nbn:de:0030-drops-114263 https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.14 eng https://creativecommons.org/licenses/by/3.0/legalcode