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

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Adamaszek, Anna, Czumaj, Artur and Lingas, Andrzej (2009) PTAS for k-tour cover problem on the plane for moderately large values of k. In: 20th International Symposium on Algorithms and Computations (ISAAC 2009), Honolulu, HI, December 16-18, 2009. Published in: Lecture Notes in Computer Science, 5878 pp. 994-1003.

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Official URL: http://dx.doi.org/10.1007/978-3-642-10631-6_100

Abstract

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 = O(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 O((k/epsilon)(O(1)) points.

Item Type:

Conference Item (Lecture)

Subjects:

Q Science > QA Mathematics
Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software

Divisions:

Faculty of Science > Computer Science

Library of Congress Subject Headings (LCSH):

Transportation problems (Programming), Approximation algorithms

Series Name:

Lecture Notes in Computer Science

Journal or Publication Title:

Lecture Notes in Computer Science

Publisher:

Springer

ISBN:

978-3-642-10630-9

ISSN:

0302-9743

Editor:

Dong, Y and Du, DZ and Ibarra, O

Official Date:

2009

Dates:

Date	Event
2009	Published

Volume:

5878

Number of Pages:

Page Range:

pp. 994-1003

Identification Number:

10.1007/978-3-642-10631-6_100

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Restricted or Subscription Access

Funder:

Engineering and Physical Sciences Research Council (EPSRC), Sweden. Vetenskapsrådet [Research Council], University of Warwick. Centre for Discrete Mathematics and Its Applications

Grant number:

EP/D063191/1 (EPSRC), 621-2005-408 (VR)

Version or Related Resource:

Also published in: Adamaszek, A., et al. (2010). PTAS for k-tour cover problem on the plane for moderately large values of k. International Journal of Foundations of Computer Science, 21(6), pp. 893-904. http://wrap.warwick.ac.uk/id/eprint/41591

Conference Paper Type:

Lecture

Title of Event:

20th International Symposium on Algorithms and Computations (ISAAC 2009)

Type of Event:

Conference

Location of Event:

Honolulu, HI

Date(s) of Event:

December 16-18, 2009

Related URLs:

Related item in WRAP

References:

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