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
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Finding the Optimal Path in 3D Spaces Using EDAs --- The Wireless Sensor Networks Scenario
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part I
Theoretical Computer Science
Proceedings of the twenty-sixth annual symposium on Computational geometry
A QPTAS for TSP with fat weakly disjoint neighborhoods in doubling metrics
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Truthful mechanisms for exhibitions
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Algorithms for interval structures with applications
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Self-organizing map for the multi-goal path planning with polygonal goals
ICANN'11 Proceedings of the 21th international conference on Artificial neural networks - Volume Part I
Minimum-perimeter intersecting polygons
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
On approximating the TSP with intersecting neighborhoods
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
On the minimum corridor connection problem and other generalized geometric problems
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Computing shortest heterochromatic monotone routes
Operations Research Letters
Visiting convex regions in a polygonal map
Robotics and Autonomous Systems
Algorithms for interval structures with applications
Theoretical Computer Science
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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.