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QPTAS for the CVRP with a Moderate Number of Routes in a Metric Space of Any Fixed Doubling Dimension

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Learning and Intelligent Optimization (LION 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12096))

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Abstract

The Capacitated Vehicle Routing Problem (CVRP) is the well-known combinatorial optimization problem having a host of valuable practical applications in operations research. The CVRP is strongly NP-hard both in its general case and even in very specific settings (e.g., on the Euclidean plane). The problem is APX-complete for an arbitrary metric and admits Quasi-Polynomial Time Approximation Scheme (QPTAS) in the Euclidean space of any fixed dimension (and even PTAS, under additional constraints). In this paper, we significantly extend the class of metric settings of the CVRP that can be approximated efficiently. We show that the metric CVRP admits QPTAS any time, when it is formulated in a metric space of a fixed doubling dimension \(d>1\) and is restricted to have an optimal solution of at most \(\mathrm {polylog}\,{n}\) routes.

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Authors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay & Yuri Ogorodnikov

  2. Ural Federal University, Ekaterinburg, Russia

    Michael Khachay & Yuri Ogorodnikov

  3. Omsk State Technical University, Omsk, Russia

    Michael Khachay

Authors
  1. Michael Khachay
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  2. Yuri Ogorodnikov
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Corresponding authors

Correspondence to Michael Khachay or Yuri Ogorodnikov .

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Editors and Affiliations

  1. CARGO Lab., Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias S. Kotsireas

  2. Center for Applied Optimization, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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Khachay, M., Ogorodnikov, Y. (2020). QPTAS for the CVRP with a Moderate Number of Routes in a Metric Space of Any Fixed Doubling Dimension. In: Kotsireas, I., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 2020. Lecture Notes in Computer Science(), vol 12096. Springer, Cham. https://doi.org/10.1007/978-3-030-53552-0_4

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