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A Quasi-Polynomial-Time Approximation Scheme for Vehicle Routing on Planar and Bounded-Genus Graphs

Authors Amariah Becker, Philip N. Klein, David Saulpic

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Amariah Becker
Philip N. Klein
David Saulpic

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Amariah Becker, Philip N. Klein, and David Saulpic. A Quasi-Polynomial-Time Approximation Scheme for Vehicle Routing on Planar and Bounded-Genus Graphs. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ESA.2017.12

Abstract

The Capacitated Vehicle Routing problem is a generalization of the Traveling Salesman problem in which a set of clients must be visited by a collection of capacitated tours. Each tour can visit at most Q clients and must start and end at a specified depot. We present the first approximation scheme for Capacitated Vehicle Routing for non-Euclidean metrics. Specifically we give a quasi-polynomial-time approximation scheme for Capacitated Vehicle Routing with fixed capacities on planar graphs. We also show how this result can be extended to bounded-genus graphs and polylogarithmic capacities, as well as to variations of the problem that include multiple depots and charging penalties for unvisited clients.
Keywords
  • Capacitated Vehicle Routing
  • Approximation Algorithms
  • Planar Graphs

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