Information Processing Letters
Approximation algorithms for the geometric covering salesman problem
Discrete Applied Mathematics
The hardness of approximation: gap location
Computational Complexity
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A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
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Information Sciences: an International Journal
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On the hardness of approximating minimization problems
Journal of the ACM (JACM)
On the approximability of the traveling salesman problem (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Vertex cover on 4-regular hyper-graphs is hard to approximate within 2 - &egr;
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A fast approximation algorithm for TSP with neighborhoods
Nordic Journal of Computing
The Complexity of Approximating the Class Steiner Tree Problem
WG '91 Proceedings of the 17th International Workshop
TSP with Neighborhoods of Varying Size
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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
Approximation algorithms for TSP with neighborhoods in the plane
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
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
Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Approximating corridors and tours via restriction and relaxation techniques
ACM Transactions on Algorithms (TALG)
Theoretical Computer Science
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Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
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
Selective graph coloring in some special classes of graphs
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Coherent image selection using a fast approximation to the generalized traveling salesman problem
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Visiting convex regions in a polygonal map
Robotics and Autonomous Systems
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We prove that various geometric covering problems related to the Traveling Salesman Problem cannot be efficiently approximated to within any constant factor unless P = NP. This includes the Group-Traveling Salesman Problem (TSP with Neighborhoods) in the Euclidean plane, the Group-Steiner-Tree in the Euclidean plane and the Minimum Watchman Tour and Minimum Watchman Path in 3-D. Some inapproximability factors are also shown for special cases of the above problems, where the size of the sets is bounded. Group-TSP and Group-Steiner-Tree where each neighborhood is connected are also considered. It is shown that approximating these variants to within any constant factor smaller than 2 is NP-hard.For the Group-Traveling Salesman and Group-Steiner-Tree Problems in dimension d, we show an inapproximability factor of O(log(d驴1)/dn) under a plausible conjecture regarding the hardness of Hyper-Graph Vertex-Cover.