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
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Linear Programming in Linear Time When the Dimension Is Fixed
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
Finding the Shortest Watchman Route in a Simple Polygon
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Balanced Partition of Minimum Spanning Trees
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
TSP with Neighborhoods of Varying Size
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Building bridges between convex regions
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Shortest paths in simple polygons with polygon-meet constraints
Information Processing Letters
TSP with neighborhoods of varying size
Journal of Algorithms
Stochastic event capture using mobile sensors subject to a quality metric
Proceedings of the 12th annual international conference on Mobile computing and networking
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Query-point visibility constrained shortest paths in simple polygons
Theoretical Computer Science
Minimum Spanning Tree with Neighborhoods
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Visiting a Polygon on the Optimal Way to a Query Point
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
TSP with neighborhoods of varying size
Journal of Algorithms
Traveling salesman problem of segments
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
On trip planning queries in spatial databases
SSTD'05 Proceedings of the 9th international conference on Advances in Spatial and Temporal Databases
Parameterized algorithms for generalized traveling salesman problems in road networks
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. As a generalization of the classical Euclidean TSP, TSPN is also NP-hard. In this paper, we present new approximation results for the TSPN, including (1) a constant-factor approximation algorithm for the case of arbitrary connected neighborhoods having comparable diameters; and (2) a PTAS for the important special case of disjoint unit disk neighborhoods (or nearly disjoint, nearly-unit disks). Our methods also yield improved approximation ratios for various special classes of neighborhoods, which have previously been studied. Further, we give a linear-time &Ogr;(1)-approximation algorithm for the case of neighborhoods that are (infinite) straight lines.