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

Adamaszek, Anna; Czumaj, Artur and Lingas, Andrzej LU (2010) In International Journal of Foundations of Computer Science 21(6). p.893-904
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 = 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),... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Approximation algorithms, capacitated vehicle routing, k-tour cover, polynomial-time approximation scheme
in
International Journal of Foundations of Computer Science
volume
21
issue
6
pages
893 - 904
publisher
World Scientific
external identifiers
  • wos:000286806000003
  • scopus:78649403560
ISSN
0129-0541
DOI
10.1142/S0129054110007623
language
English
LU publication?
yes
id
1b34a2c3-6b7e-4836-a9f7-50f22151f8cb (old id 1859794)
date added to LUP
2011-04-20 08:50:33
date last changed
2018-05-29 12:24:45
@article{1b34a2c3-6b7e-4836-a9f7-50f22151f8cb,
  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 = 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 &lt;= 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.},
  author       = {Adamaszek, Anna and Czumaj, Artur and Lingas, Andrzej},
  issn         = {0129-0541},
  keyword      = {Approximation algorithms,capacitated vehicle routing,k-tour cover,polynomial-time approximation scheme},
  language     = {eng},
  number       = {6},
  pages        = {893--904},
  publisher    = {World Scientific},
  series       = {International Journal of Foundations of Computer Science},
  title        = {PTAS for k-tour cover poblem on the plane for moderately large values of k},
  url          = {http://dx.doi.org/10.1142/S0129054110007623},
  volume       = {21},
  year         = {2010},
}