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

In a generalized intersection searching problem, a set, S, of colored geometrie objects is to be preprocessed so that given some query object, q, the distinct colors of the objects intersected by q can be reported efficiently or the number of such colors can be counted effi.ciently. In the dynamic setting, colored objects can be inserted into or de1eted from S. These problems generalize the well-studied standard intersection searching problems and are rich in applications. Unfortunate1y, the techniques known for the standard problems do not yie1d efficient solutions for the generalized problems. Moreover, previous work [JL92] on generalized problems applies only to the static reporting problems. In thispaper, a uniform framework is presented to solve efficiently the countingjreportingj dynamic versions of a variety of generalized intersection searching problems, including: 1-, 2-, and 3-dimensional range searching, quadrant searching, interval intersection searching, 1and 2-dimensional point enclosure searching, and orthogonal segment intersection searching.