Space Efficient Dynamic Orthogonal Range Reporting

Abstract

In this paper we present new space efficient dynamic data structures for orthogonal range reporting. The described data structures support planar range reporting queries in time O(log n+klog log (4n/(k+1))) and space O(nlog log n), or in time O(log n+k) and space O(nlog en) for any e>0. Both data structures can be constructed in O(nlog n) time and support insert and delete operations in amortized time O(log 2n) and O(log nlog log n) respectively. These results match the corresponding upper space bounds of Chazelle (SIAM J. Comput. 17, 427–462, 1988) for the static case. We also present a dynamic data structure for d-dimensional range reporting with search time O(log d−1n+k), update time O(log dn), and space O(nlog d−2+en) for any e>0. The model of computation used in our paper is a unit cost RAM with word size log n.