Computing Point Enclosures

Abstract

Given a set of n rectangles in the plane, the point enclosure query is the question to determine for any point p which rectangles of the set it is contained in. It is the "dual" of the well-known range query in computational geometry. It is shown that the point enclosure query in the plane can be answered in 0(log n + k) time, where k is the number of rectangles reported. The solution makes use of a new data structure, called the S-tree. The data structure can be generalized to obtain an efficient algorithm for the point enclosure problem in d-dimensional space d ≥ 2.