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.

The Colored Sector Search Tree: A Dynamic Data Structure for Efficient High Dimensional Nearest-Foreign-Neighbor Queries

Given a set S of n points in R/sup D/, D/spl ges/2. Each point p/spl isin/S is assigned a color c(p) chosen from a fixed color set. The All-Nearest-Foreign-Neighbors Problem (ANFNP) is to find for each point p/spl isin/S its nearest foreign neighbors, i.e. the set of all points in S/{p} that are closest to p among the points in S with a color different from c(p). We introduce the Well Separated Color Decomposition (WSCD) which gives an optimal O(log n) parallel algorithm to solve the AMFNP, for fixed dimension D/spl ges/2 and fixed L/sup t/-metric d/sub t/, 1/spl les/t/spl les//spl infin/. The WSCD is based upon the Well Separated Pair Decomposition (Callahan et al., 1992). The ANFNP finds extensive applications in VLSI design and verification for two dimensions, and in traffic-control systems and Geographic Information Systems for D>2 dimensions. To the best of our knowledge, this is the only known optimal parallel algorithm for the ANFNP.

N. S. Janaki Latha

Papers

An optimal parallel algorithm for the all-nearest-foreign-neighbors problem in arbitrary dimensions

The Colored Sector Search Tree: A Dynamic Data Structure for Efficient High Dimensional Nearest-Foreign-Neighbor Queries