TSP with neighborhoods of varying size
de Berg, M ; Gudmundsson, J ; Katz, MJ ; Levcopoulos, Christos LU
; Overmars, MH
and van der Stappen, AF
(2005)
In Journal of Algorithms
57(1).
p.22-36
- Abstract
- In TSP with neighborhoods (TSPN) we are given a collection S of regions in the plane, called neighborhoods, and we seek the shortest tour that visits all neighborhoods. Until now constant-factor approximation algorithms have been known only for cases where the neighborhoods are of approximately the same size. In this paper we present the first polynomial-time constant-factor approximation algorithm for disjoint convex fat neighborhoods of arbitrary size. We also show that in the general case, where the neighborhoods can overlap and are not required to be convex or fat, TSPN is APX-hard and cannot be approximated within a factor of 391/390 in polynomial time, unless P = NP.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/221400
- author
- de Berg, M
; Gudmundsson, J
; Katz, MJ
; Levcopoulos, Christos
LU
; Overmars, MH
and van der Stappen, AF
- organization
- publishing date
- 2005
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- approximation algorithms, TSP with neighborhoods, computational geometry
- in
- Journal of Algorithms
- volume
- 57
- issue
- 1
- pages
- 22 - 36
- publisher
- Elsevier
- external identifiers
-
- wos:000232283200002
- scopus:24944449883
- ISSN
- 1090-2678
- DOI
- 10.1016/j.jalgor.2005.01.010
- project
- VR 2002-4049
- language
- English
- LU publication?
- yes
- id
- cbf6256e-ca25-4a76-8736-0f7e6fbde4be (old id 221400)
- date added to LUP
- 2016-04-01 12:08:19
- date last changed
- 2022-04-13 06:38:11
@article{cbf6256e-ca25-4a76-8736-0f7e6fbde4be,
abstract = {{In TSP with neighborhoods (TSPN) we are given a collection S of regions in the plane, called neighborhoods, and we seek the shortest tour that visits all neighborhoods. Until now constant-factor approximation algorithms have been known only for cases where the neighborhoods are of approximately the same size. In this paper we present the first polynomial-time constant-factor approximation algorithm for disjoint convex fat neighborhoods of arbitrary size. We also show that in the general case, where the neighborhoods can overlap and are not required to be convex or fat, TSPN is APX-hard and cannot be approximated within a factor of 391/390 in polynomial time, unless P = NP.}},
author = {{de Berg, M and Gudmundsson, J and Katz, MJ and Levcopoulos, Christos and Overmars, MH and van der Stappen, AF}},
issn = {{1090-2678}},
keywords = {{approximation algorithms; TSP with neighborhoods; computational geometry}},
language = {{eng}},
number = {{1}},
pages = {{22--36}},
publisher = {{Elsevier}},
series = {{Journal of Algorithms}},
title = {{TSP with neighborhoods of varying size}},
url = {{http://dx.doi.org/10.1016/j.jalgor.2005.01.010}},
doi = {{10.1016/j.jalgor.2005.01.010}},
volume = {{57}},
year = {{2005}},
}