Efficient Dynamic Range Searching using Data Replication

Given the lower bound of\Omega\Gamma n (d\Gamma1)=d ) for range query time complexity on n d-dimensional point data, we investigate whether little replication can improve the query and update times significantly. We propose linear-space index structures that minimize the query and update times; the query time we achieve is O(n ffl ) for any ffl ? 0, and, the update time is O(log n). 1 Introduction Given a set S of d-dimensional points, a range query q is specified by d 1-dimensional intervals [a i ; b i ] one for each dimension i, and retrieves all points p = (p 1 ; p 2 ; : : : p d ) in S such that h8i 2 f1; : : : ; dg : a i p i b i i. This type of searching in multiple dimensions is fundamental to geographic information systems, image databases and computer graphics. Several efficient data structures using linear and nonlinear space (measured in terms of the number of data points) have been proposed in the literature [Bentley 1977, Bentley 1980, Guttman 1984]. For large databa..