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PTAS for ktour 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 ktour cover problem on the plane for moderately large values of k. In: 20th International Symposium on Algorithms and Computations (ISAAC 2009), Honolulu, HI, December 1618, 2009. Published in: Lecture Notes in Computer Science, 5878 pp. 9941003.
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Official URL: http://dx.doi.org/10.1007/9783642106316_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 ktour 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 ktour cover problem is known to be NPhard. It is also known to admit constant factor approximation algorithms for all values of k and even a polynomialtime 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 ktour 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:  9783642106309  
ISSN:  03029743  
Editor:  Dong, Y and Du, DZ and Ibarra, O  
Official Date:  2009  
Dates: 


Volume:  5878  
Number of Pages:  10  
Page Range:  pp. 9941003  
Identifier:  10.1007/9783642106316_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), 6212005408 (VR)  
Version or Related Resource:  Also published in: Adamaszek, A., et al. (2010). PTAS for ktour cover problem on the plane for moderately large values of k. International Journal of Foundations of Computer Science, 21(6), pp. 893904. 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 1618, 2009  
Related URLs:  
References:  1. Arora, S.: Polynomial time approximation schemes for Euclidean traveling salesman 

URI:  http://wrap.warwick.ac.uk/id/eprint/5481 
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