%0 Report
%D 2003
%T Fast Algorithms for 3-D Dominance Reporting and Counting
%A Shi,Qingmin
%A JaJa, Joseph F.
%K Technical Report
%X 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
%I Instititue for Advanced Computer Studies, Univ of Maryland, College Park
%V UMIACS-TR-2003-06
%8 2003/02/05/
%G eng
%U http://drum.lib.umd.edu/handle/1903/1253