Efficient worst-case data structures for range searching

In this paper we investigate the worst-case complexity of range searching: preprocess N points in k-space such that range queries can be answered quickly. A range query asks for all points with each coordinate in some range of values, and arises in many problems in statistics and data bases. We develop three different structures for range searching in this paper. The first structure has absolutely optimal query time (which we prove), but has very high preprocessing and storage costs. The second structure we present has logarithmic query time and O(N¹⁺²) preprocessing and storage costs, for any fixed >0. Finally we give a structure with linear storage, O(N ln N) preprocessing and O(N) query time.Research in this paper has been supported partially under Office of Naval Research contract N000014-76-C-0373, USA, and by the Austrian Federal Ministry for Science and Research