TY - JOUR
T1 - TSP with neighborhoods of varying size
AU - De Berg, Mark
AU - Gudmundsson, Joachim
AU - Katz, Matthew J.
AU - Levcopoulos, Christos
AU - Overmars, Mark H.
AU - Van Der Stappen, A. Frank
N1 - Funding Information:
* Corresponding author. E-mail addresses: m.t.d.berg@tue.nl (M. de Berg), joachim.gudmundsson@nicta.com.au (J. Gudmundsson), matya@cs.bgu.ac.il (M.J. Katz), christos@cs.lth.se (C. Levcopoulos), markov@cs.uu.nl (M.H. Overmars), frankst@cs.uu.nl (A.F. van der Stappen). 1 National ICT Australia is funded by the Australian Government’s Backing Australia’s Ability initiative, in part through the Australian Research Council. 2 Supported by grant no. 2000160 from the US–Israel Binational Science Foundation.
PY - 2005/9/1
Y1 - 2005/9/1
N2 - 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.
AB - 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.
KW - Approximation algorithms
KW - Computational geometry
KW - TSP with neighborhoods
UR - http://www.scopus.com/inward/record.url?scp=24944449883&partnerID=8YFLogxK
U2 - 10.1016/j.jalgor.2005.01.010
DO - 10.1016/j.jalgor.2005.01.010
M3 - Article
AN - SCOPUS:24944449883
SN - 0196-6774
VL - 57
SP - 22
EP - 36
JO - Journal of Algorithms
JF - Journal of Algorithms
IS - 1
ER -