Further Results on Generalized Intersection Searching Problems: Counting, Reporting, and Dynamization

In a generalized intersection searching problem, a set, S, of colored geometric objects is to be preprocessed so that given some query object, q, the distinct colors of the objects intersected by q can be reported or counted efficiently. In the dynamic setting, colored objects can be inserted into or deleted from S. These problems generalize the well-studied standard intersection searching problems and are rich in applications. Unfortunately, the techniques known for the standard problems do not yield efficient solutions for the generalized problems. Moreover, previous work on generalized problems applies only to the reporting problems and that too mainly to the static case. In this paper, a uniform framework is presented to solve efficiently the counting/reporting/dynamic versions of a variety of generalized intersection searching problems, including: 1-, 2-, and 3-dimensional range searching, quadrant searching, and 2-dimensional point enclosure searching. Several other related results are also mentioned.