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Efficient approximation of the metric CVRP in spaces of fixed doubling dimension

Author

Listed:
  • Michael Khachay

    (Krasovsky Institute of Mathematics and Mechanics
    Ural Federal University)

  • Yuri Ogorodnikov

    (Krasovsky Institute of Mathematics and Mechanics
    Ural Federal University)

  • Daniel Khachay

    (KEDGE Business School)

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 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 Das and 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 $$d>1$$ d > 1 and the capacity does not exceed $$\mathrm {polylog}{(n)}$$ polylog ( n ) .

Suggested Citation

  • Michael Khachay & Yuri Ogorodnikov & Daniel Khachay, 2021. "Efficient approximation of the metric CVRP in spaces of fixed doubling dimension," Journal of Global Optimization, Springer, vol. 80(3), pages 679-710, July.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:3:d:10.1007_s10898-020-00990-0
    DOI: 10.1007/s10898-020-00990-0
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    References listed on IDEAS

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