A Tight 4/3 Approximation for Capacitated Vehicle Routing in Trees

Author Amariah Becker

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Amariah Becker
  • Brown University Department of Computer Science, Providence, RI, USA

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Amariah Becker. A Tight 4/3 Approximation for Capacitated Vehicle Routing in Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Given a set of clients with demands, the Capacitated Vehicle Routing problem is to find a set of tours that collectively cover all client demand, such that the capacity of each vehicle is not exceeded and such that the sum of the tour lengths is minimized. In this paper, we provide a 4/3-approximation algorithm for Capacitated Vehicle Routing on trees, improving over the previous best-known approximation ratio of (sqrt{41}-1)/4 by Asano et al.[Asano et al., 2001], while using the same lower bound. Asano et al. show that there exist instances whose optimal cost is 4/3 times this lower bound. Notably, our 4/3 approximation ratio is therefore tight for this lower bound, achieving the best-possible performance.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
  • Approximation algorithms
  • Graph algorithms
  • Capacitated vehicle routing


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