Computational geometry: an introduction
Computational geometry: an introduction
Average case analysis of dynamic geometric optimization
Computational Geometry: Theory and Applications
Location Privacy in Pervasive Computing
IEEE Pervasive Computing
Tight Error Bounds of Geometric Problems on Convex Objects with Imprecise Coordinates
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Capturing the Uncertainty of Moving-Object Representations
SSD '99 Proceedings of the 6th International Symposium on Advances in Spatial Databases
Smallest Color-Spanning Objects
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Convex Hulls of Bounded Curvature
Proceedings of the 8th Canadian Conference on Computational Geometry
Querying Imprecise Data in Moving Object Environments
IEEE Transactions on Knowledge and Data Engineering
Probabilistic skylines on uncertain data
VLDB '07 Proceedings of the 33rd international conference on Very large data bases
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Dynamic half-space reporting, geometric optimization, and minimum spanning trees
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Keyword Search in Spatial Databases: Towards Searching by Document
ICDE '09 Proceedings of the 2009 IEEE International Conference on Data Engineering
Probabilistic Reverse Nearest Neighbor Queries on Uncertain Data
IEEE Transactions on Knowledge and Data Engineering
Superseding Nearest Neighbor Search on Uncertain Spatial Databases
IEEE Transactions on Knowledge and Data Engineering
Computing minimum diameter color-spanning sets
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Preserving user location privacy in mobile data management infrastructures
PET'06 Proceedings of the 6th international conference on Privacy Enhancing Technologies
Largest bounding box, smallest diameter, and related problems on imprecise points
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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In this paper we study several geometric problems of color-spanning sets: given n points with m colors in the plane, selecting m points with m distinct colors such that some geometric properties of the m selected points are minimized or maximized. The geometric properties studied in this paper are the maximum diameter, the largest closest pair, the planar smallest minimum spanning tree, the planar largest minimum spanning tree and the planar smallest perimeter convex hull. We propose an O(n 1+驴 ) time algorithm for the maximum diameter color-spanning set problem where 驴 could be an arbitrarily small positive constant. Then, we present hardness proofs for the other problems and propose two efficient constant factor approximation algorithms for the planar smallest perimeter color-spanning convex hull problem.