Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A note on relative neighborhood graphs
SCG '87 Proceedings of the third annual symposium on Computational geometry
A linear time algorithm for finding all farthest neighbors in a convex polygon
Information Processing Letters
Quasi-Valid range querying and its implications for nearest neighbor problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Optimal parallel algorithms for polygon and point-set problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
On Finding the Maxima of a Set of Vectors
Journal of the ACM (JACM)
On the Average Number of Maxima in a Set of Vectors and Applications
Journal of the ACM (JACM)
The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees
Journal of the ACM (JACM)
Multidimensional divide-and-conquer
Communications of the ACM
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We present an &Ogr;(N log2 N) divide-and-conquer algorithm for solving the all pairs geographic nearest neighbor problem (GNN) for a set of N sites in the plane under any Lp metric, 1 ≤ p ≥ ∞. This algorithm uses the monotone matrix searching technique of Aggarwal et. al. In addition, our method yields an &Ogr;(N logd-1 N) expected time algorithm for the d-dimensional GNN problem. We also discuss the applications of GNN approach to rectilinear Steiner trees.