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Fourth International Conference on High-Performance Computing
An optimal parallel algorithm for the all-nearest-foreign-neighbors problem in arbitrary dimensions
Bangalore, India
December 18-December 21
ISBN: 0-8186-8067-9
T. Graf, Research Centre J?
N. S. Janaki Latha, Indian Institute of Technology
V. Kamakoti, Indian Institute of Science
C. Pandu Rangan, Indian Institute of Technology
Given a set S of n points in IRD, D \ge 2. Each point p \in S is assigned acolor c(p) chosen from a fixed color set. The All-Nearest-Foreign-Neighbors Problem (ANFNP) is to find for each point p \in 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 ANFNP, for fixed dimension D \ge 2 and fixed Lt-metric dt, 1 \le t \le \infty. The WSCD is based upon the Well Separated Pair Decomposition ([5]). The ANFNP finds extensive applications in VLSI design and verification ([11]) for two dimensions, and in traffic-control systems and Geographic Information Systems (GIS) ([7, 12, 13, 14, 15]) for D > 2 dimensions. To the best of our knowledge, this is the only known optimal parallel algorithm for the ANFNP.
Index Terms:
Closest Pair, Closest Foreign Pair, Computational Geometry, Parallel Algorithms
Citation:
T. Graf, N. S. Janaki Latha, V. Kamakoti, C. Pandu Rangan, "An optimal parallel algorithm for the all-nearest-foreign-neighbors problem in arbitrary dimensions," hipc, pp.132, Fourth International Conference on High-Performance Computing, 1997
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