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PTAS for k-tour cover poblem on the plane for moderately large values of k

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Author

Summary, in English

Let P be a set of n points in the Euclidean plane and let O be the origin point in the plane. In the k-tour cover problem (called frequently the capacitated vehicle routing problem), the goal is to minimize the total length of tours that cover all points in P, such that each tour starts and ends in O and covers at most k points from P. The k-tour cover problem is known to be NP-hard. It is also known to admit constant factor approximation algorithms for all values of k and even a polynomial-time approximation scheme (PTAS) for small values of k, k = circle divide (log n/ log log n). In this paper, we significantly enlarge the set of values of k for which a PTAS is provable. We present a new PTAS for all values of k <= 2(log delta n), where delta = delta(epsilon). The main technical result proved in the paper is a novel reduction of the k-tour cover problem with a set of n points to a small set of instances of the problem, each with circle divide((k/epsilon)(circle divide(1))) points.

Department/s

  • Computer Science

Publishing year

2010

Language

English

Pages

893-904

Publication/Series

International Journal of Foundations of Computer Science

Volume

21

Issue

6

Document type

Journal article

Publisher

World Scientific Publishing

Topic

  • Computer Science

Keywords

  • Approximation algorithms
  • capacitated vehicle routing
  • k-tour cover
  • polynomial-time approximation scheme

Status

Published

ISBN/ISSN/Other

  • ISSN: 0129-0541