An optimal parallel algorithm for the all-nearest-foreign-neighbors problem in arbitrary dimensions
نویسندگان
چکیده
Given a set S of n points in IR D , D 2. Each point p 2 S is assigned a color c(p) chosen from a xed color set. The All-Nearest-Foreign-Neighbors Problem (ANFNP) is to nd for each point p 2 S its nearest foreign neighbors, i.e. the set of all points in Snfpg that are closest to p among the points in S with a color diierent from c(p). We introduce the Well Separated Color Decomposition (WSCD) which gives an optimal O(log n) parallel algorithm to solve the ANFNP, for xed dimension D 2 and xed L t-metric d t , 1 t 1. The WSCD is based upon the Well Separated Pair Decomposition ((5]). The ANFNP nds extensive applications in VLSI design and veriica-tion ((11]) for two dimensions, and in traac-control systems and Geographic Information Systems (GIS) best of our knowledge, this is the only known optimal parallel algorithm for the ANFNP.
منابع مشابه
Non-zero probability of nearest neighbor searching
Nearest Neighbor (NN) searching is a challenging problem in data management and has been widely studied in data mining, pattern recognition and computational geometry. The goal of NN searching is efficiently reporting the nearest data to a given object as a query. In most of the studies both the data and query are assumed to be precise, however, due to the real applications of NN searching, suc...
متن کاملAn Optimal Parallel Algorithm For the All Nearest -- Neighbor Problem for a Convex Polygon
In this paper we give a parallel algorithm for finding the nearest-neighbor vertex of each vertex of a convex polygon. Our algoritb..z::J. runs in O(log n) time using O(njlogn) processors, in the parallel computation model CREW PRA.lvr (ConcurrentRead, Exclusive-Write Parallel RAM). This implies that the all nearest-neighbors problem for a convex polygon can be solved in O(n/p+logn) time using ...
متن کاملParallel Algorithms for Nearest Neighbor Search Problems in High Dimensions
The nearest neighbor search problem in general dimensions finds application in computational geometry, computational statistics, pattern recognition, and machine learning. Although there is a significant body of work on theory and algorithms, surprisingly little work has been done on algorithms for high-end computing platforms and no open source library exists that can scale efficiently to thou...
متن کاملOptimal Mesh Computer Algorithms for Simple Polygons
We present optimal parallel algorithms that run in O(p n) time on a p n p n mesh-connected computer for a number of fundamental problems concerning visibility and distance properties inside a simple polygon. These include computing shortest paths, shortest path trees, shortest path partitions, all-farthest neighbors (both internal and external), the visibility polygon of a point, the weak visib...
متن کاملOptimal Parallel All-Nearest-Neighbors Using the Well-Separated Pair Decomposition (Preliminary Version)
We present an optimal parallel algorithm to construct the well-separated pair decomposition of a point set P in < d. We show how this leads to a deterministic optimal O(logn) time parallel algorithm for nding the k-nearest-neighbors of each point in P, where k is a constant. We discuss several additional applications of the well-separated pair decomposition for which we can derive faster parall...
متن کامل