Approximation algorithms for the geometric covering salesman problem
Discrete Applied Mathematics
Approximation algorithms for geometric tour and network design problems (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Approximating geometrical graphs via “spanners” and “banyans”
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Handbook of discrete and computational geometry
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A fast approximation algorithm for TSP with neighborhoods
Nordic Journal of Computing
Approximation algorithms for TSP with neighborhoods in the plane
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
TSP with neighborhoods of varying size
Journal of Algorithms
Approximation algorithms for euclidean group TSP
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On approximating the TSP with intersecting neighborhoods
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Minimum Spanning Tree with Neighborhoods
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
On the minimum corridor connection problem and other generalized geometric problems
Computational Geometry: Theory and Applications
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
Minimum Covering with Travel Cost
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Data gathering tours for mobile robots
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
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
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Minimum perimeter convex hull of imprecise points in convex regions
Proceedings of the twenty-seventh annual symposium on Computational geometry
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
On approximating the TSP with intersecting neighborhoods
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Efficient data collection from wireless nodes under the two-ring communication model
International Journal of Robotics Research
The traveling salesman problem: low-dimensionality implies a polynomial time approximation scheme
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Computing shortest heterochromatic monotone routes
Operations Research Letters
Minimum covering with travel cost
Journal of Combinatorial Optimization
Controlled mobility in stochastic and dynamic wireless networks
Queueing Systems: Theory and Applications
Algorithms for interval structures with applications
Theoretical Computer Science
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The Euclidean TSP with neighborhoods (TSPN) problem seeks a shortest tour that visits a given collection of n regions (neighborhoods). We present the first polynomial-time approximation scheme for TSPN for a set of regions given by arbitrary disjoint fat regions in the plane. This improves substantially upon the known approximation algorithms, and is the first PTAS for TSPN on regions of non-comparable sizes. Our result is based on a novel extension of the m-guillotine method. The result applies to regions that are "fat" in a very weak sense: each region Pi contains a disk of radius Ω(diam(Pi)), but is otherwise arbitrary. Further, the result applies even if the regions intersect arbitrarily, provided that there exists a packing of disjoint disks, of radii Ω(diam(Pi)), contained within their respective regions. Finally, the PTAS result applies also to the case in which the regions are sets of points or polygons, each each lying within one of a given set of disjoint fat regions.