Fast Algorithms For 3-D Dominance Reporting And Counting

We present in this paper fast algorithms for the 3-D dominance reporting and counting problems, and generalize the results to the d-dimensional case. Our 3-D dominance reporting algorithm achieves O(log n= log log n + f) 1 query time using O(n log n) space , where f is the number of points satisfying the query and > 0 is an arbitrarily small constant. For the 3-D dominance counting problem (which is equivalent to the 3-D range counting problem), our algorithm runs in O((log n= log log n) 2) time using O(nlog 1+ n= log log n) space.