An improved algorithm for static 3D dominance reporting in the pointer machine

Abstract

We present an efficient algorithm for the pointer machine model that preprocesses a set of n three-dimensional points in O(n log n) worst case time to construct an O(n) space data structure that supports three-dimensional dominance reporting queries in O(log n+t) worst case time, when t points are reported. Previous results achieved either O(n2) worst case or O(n log n) expected preprocessing time. The novelty of our approach is that we employ persistent data structures and exploit geometric observations of previous works, in order to achieve a drastic reduction in the worst case preprocessing time. © Springer-Verlag Berlin Heidelberg 2012.