PTAS for k-tour cover poblem on the plane for moderately large values of k
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1859794
- author
- Adamaszek, Anna ; Czumaj, Artur and Lingas, Andrzej LU
- organization
- publishing date
- 2010
- 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 Publishing
- 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
- 2016-04-01 09:58:17
- date last changed
- 2022-04-27 17:23:26
@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 <= 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}}, keywords = {{Approximation algorithms; capacitated vehicle routing; k-tour cover; polynomial-time approximation scheme}}, language = {{eng}}, number = {{6}}, pages = {{893--904}}, publisher = {{World Scientific Publishing}}, 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}}, doi = {{10.1142/S0129054110007623}}, volume = {{21}}, year = {{2010}}, }