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. ISBN 978-3-642-10630-9. doi:10.1007/978-3-642-10631-6_100 ISSN 0302-9743.

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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, Engineering and Medicine > 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:	10
Page Range:	pp. 994-1003
DOI:	10.1007/978-3-642-10631-6_100
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	3 December 2015
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

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