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

In English

Författare

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.

Avdelning/ar

  • Computer Science

Publiceringsår

2010

Språk

Engelska

Sidor

893-904

Publikation/Tidskrift/Serie

International Journal of Foundations of Computer Science

Volym

21

Issue

6

Dokumenttyp

Artikel i tidskrift

Förlag

World Scientific Publishing

Ämne

  • Computer Science

Nyckelord

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

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 0129-0541