COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
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Given a set S of n points in IRD, D \ge 2. Eachpoint p \in S is assigned acolor c(p) chosen from a fixedcolor 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 colordifferent from c(p). We introduce the Well SeparatedColor 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 findsextensive applications in VLSI design and verification ([11]) for two dimensions, and in traffic-controlsystems and Geographic Information Systems (GIS)([7, 12, 13, 14, 15]) for D 2 dimensions. To thebest of our knowledge, this is the only known optimalparallel algorithm for the ANFNP.