TSP with Neighborhoods of Varying Size

Authors:
Mark de Berg;Joachim Gudmundsson;Matthew J. Katz;Christos Levcopoulos;Mark H. Overmars;A. Frank van der Stappen
Affiliations:
-;-;-;-;-;-
Venue:
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Year:
2002

Citing 13
Cited 3

Fat triangles determine linearly many holes

SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A pedestrian approach to ray shooting: shoot a ray, take a walk

SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Approximation algorithms for the geometric covering salesman problem

Discrete Applied Mathematics
Computing depth orders for fat objects and related problems

Computational Geometry: Theory and Applications
Approximation algorithms for geometric tour and network design problems (extended abstract)

Proceedings of the eleventh annual symposium on Computational geometry
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems

Journal of the ACM (JACM)
Guillotine Subdivisions Approximate Polygonal Subdivisions: A Simple Polynomial-Time Approximation Scheme for Geometric TSP, k-MST, and Related Problems

SIAM Journal on Computing
Approximation algorithms for TSP with neighborhoods in the plane

SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Walking around fat obstacles

Information Processing Letters
A fast approximation algorithm for TSP with neighborhoods

Nordic Journal of Computing
On Fat Partitioning, Fat Covering and the Union Size of Polygons (Extended Abstract)

WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Beyond Steiner's Problem: A VLSI Oriented Generalization

WG '89 Proceedings of the 15th International Workshop on Graph-Theoretic Concepts in Computer Science
Some NP-complete geometric problems

STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing

Approximation algorithms for TSP with neighborhoods in the plane

Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
On the complexity of approximating tsp with neighborhoods and related problems

Computational Complexity
Approximation algorithms for euclidean group TSP

ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming

Quantified Score

Hi-index	0.00

Visualization

Abstract

In TSP with neighborhoods we are given a set of objects 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 objects are of approximately the same size. We present the first polynomial-time constant-factor approximation algorithm for disjoint convex fat objects of arbitrary size. We also show that the problem is APX-hard and cannot be approximated within a factor of 391/390 in polynomial time, unless P = NP.