A new class of geometric intersection searching problems is introduced, which generalizes previously-considered intersection searching problems and is rich in applications. In a standard intersection searching problem, a set S of n geometric objects is to be preprocessed so that the objects that are intersected by a query object q can be reported efficiently. In a generalized problem, the objects in S come aggregated in disjoint groups and what is of interest are the groups, not the objects, that are intersected by q. Although this problem can be solved easily by using an algorithm for the standard problem, the query time can be Ω(n) even though the output size is just O(1). In this paper, algorithms with efficient, output-size-sensitive query times are presented for the generalized versions of a number of intersection searching problems, including: interval intersection searching, orthogonal segment intersection searching, orthogonal range searching, point enclosure searching, rectangle intersection searching, and segment intersection searching. In addition, the algorithms are also space-efficient.
Orthogonal range searching in linear and almost-linear space
