The Colored Quadrant Priority Search Tree with an Application to the all-nearest-foreign-neighbors Problem
نویسندگان
چکیده
Consider a dynamic set of points in the plane having different colors. Let K1 and K2 be two keys according to which points may be sorted, e.g. the xand the y-coordinate. A point p ∈ S is called proper with respect to a query point p0 ∈ S iff K1(p0) < K1(p), K2(p0) < K2(p), and if p has a different color than p0. We present the colored quadrant priority search tree (CQPST) which supports the efficient search for all k proper points in O(log n+ k) time and for the minimal proper point with respect to key K2 in O(log n) time. As an application we show that the CQPST can be used to solve the allnearest-foreign neigbors problem with respect to any arbitrary L-metric (1 ≤ t ≤ ∞) in optimal O(n log n) time.
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