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An Extension of the Das and Mathieu QPTAS to the Case of Polylog Capacity Constrained CVRP in Metric Spaces of a Fixed Doubling Dimension

  • Michael KhachayEmail author
  • Yuri Ogorodnikov
  • Daniel Khachay
Conference paper
  • 203 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12095)

Abstract

The Capacitated Vehicle Routing Problem (CVRP) is the well-known combinatorial optimization problem having numerous practically important applications. CVRP is strongly NP-hard (even on the Euclidean plane), hard to approximate in the general case and APX-complete for an arbitrary metric. Meanwhile, for the geometric settings of the problem, there are known a number of quasi-polynomial and even polynomial time approximation schemes. Among these results, the well-known QPTAS proposed by A. Das and C. Mathieu appears to be the most general. In this paper, we propose the first extension of this scheme to a more wide class of metric spaces. Actually, we show that the metric CVRP has a QPTAS any time when the problem is set up in the metric space of any fixed doubling dimension \(d>1\) and the capacity does not exceed \(\mathrm {polylog}\,{(}n)\).

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Krasovsky Institute of Mathematics and MechanicsEkaterinburgRussia
  2. 2.Ural Federal UniversityEkaterinburgRussia
  3. 3.Omsk State Technical UniversityOmskRussia

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