Compact and succinct data structures for multidimensional orthogonal range searching

Abstract

We introduce compact and succinct representations of a d-dimensional point set for any constant d≥3 supporting orthogonal range searching. Our first data structure uses dnlg⁡n+o(nlg⁡n) bits, where n denotes the number of points in P, and supporting reporting queries in O((n(d−2)/d+occ)lg⁡n/lg⁡lg⁡n) time, and counting queries in O(n(d−2)/dlg⁡n/lg⁡lg⁡n) time, where occ denotes the number of point to report, which is faster than known algorithms. Our second data structure uses dnlg⁡U−nlg⁡n+o(nlg⁡n) bits, where U is the size of the universe, which asymptotically matches the information-theoretic lower bound. The query time complexity is worse than the first one, but the algorithm runs fast in practical database search.