Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Computational geometry: an introduction
Computational geometry: an introduction
Optimal time bounds for some proximity problems in the plane
Information Processing Letters
Three Dimensional Applications in Geographical Information Systems
Three Dimensional Applications in Geographical Information Systems
An efficient randomized algorithm for the closest pair problem on colored point sets
Nordic Journal of Computing
An optimal parallel algorithm for the all-nearest-foreign-neighbors problem in arbitrary dimensions
HIPC '97 Proceedings of the Fourth International Conference on High-Performance Computing
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In this paper we present the new data structure Colored Sector Search Tree (CSST) for solving the Nearest-Foreign-Neighbor Query Problem (NFNQP): Given a set S of n colored points in RD, where D ≥ 2 is a constant, and a subset S′ ⊂ S stored in a CSST, for any colored query point q ∈ RD a nearest foreign neighbor in S′, i.e. a closest point with a different color, can be reported in O(log n(log log n)D-1) time w.r.t. a polyhedral distance function that is defined by a star-shaped polyhedron with O(1) vertices; note that this includes the Minkowski metrics d1 and d∞. It takes a preprocessing time of O(n(log n)D-1) to construct the CSST. Points from S can be inserted into the set S′ and removed from S′ in O(log n(log log n)D-1) time. The CSST uses O(n(log n)D-1) space. We present an application of the data structure in the parallel simulation of solute transport in aquifer systems by particle tracking. Other applications may be found in GIS (geo information systems) and in CAD (computer aided design). To our knowledge the CSST is the first data structure to be reported for the NFNQP.