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.


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    Title :

    An Asymptotically Optimal Approximation Algorithm for the Travelling Car Renter Problem




    Publication date :

    2019-11-15


    Size :

    15 pages , 453138 byte


    Remarks:

    OASIcs, Vol. 75, 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019), pages 14:1-14:15





    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English





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