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)
Approximation algorithms for TSP with neighborhoods in the plane
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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
A PTAS for TSP with neighborhoods among fat regions in the plane
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On the minimum corridor connection problem and other generalized geometric problems
Computational Geometry: Theory and Applications
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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.