Abstract
In this paper we study several routing problems that generalize shortest paths and the Traveling Salesman Problem. We consider a more general model that incorporates the actual cost in terms of gas prices. We have a vehicle with a given tank capacity. We assume that at each vertex gas may be purchased at a certain price. The objective is to find the cheapest route to go from s to t, or the cheapest tour visiting a given set of locations. Surprisingly, the problem of find the cheapest way to go from s to t can be solved in polynomial time and is not NP-complete. For most other versions however, the problem is NP-complete and we develop polynomial time approximation algorithms for these versions.
Research supported by NSF grant CCF-0430650. Full version available at http://www.cs.umd.edu/~samir/grant/esa07.ps
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Khuller, S., Malekian, A., Mestre, J. (2007). To Fill or Not to Fill: The Gas Station Problem. In: Arge, L., Hoffmann, M., Welzl, E. (eds) Algorithms – ESA 2007. ESA 2007. Lecture Notes in Computer Science, vol 4698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75520-3_48
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DOI: https://doi.org/10.1007/978-3-540-75520-3_48
Publisher Name: Springer, Berlin, Heidelberg
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