# Fast Algorithms for 3-D Dominance Reporting and Counting

 Title Fast Algorithms for 3-D Dominance Reporting and Counting Publication Type Reports Year of Publication 2003 Authors Shi Q, JaJa JF Date Published 2003/02/05/ Institution Instititue for Advanced Computer Studies, Univ of Maryland, College Park Keywords Technical Report Abstract We present in this paper fast algorithms for the 3-D dominance reportingand counting problems, and generalize the results to the d-dimensional case. Our 3-D dominance reporting algorithm achieves $O(\log n/\log\log n +f)$ query time using $O(n\log^{\epsilon}n)$ space, where $f$ is the number of points satisfying the query and $\epsilon>0$ is an arbitrary 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 $O(nlog^{1+\epsilon}n/\log\log n)$ space. Also UMIACS-TR-2003-06 URL http://drum.lib.umd.edu/handle/1903/1253