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.
KeywordsComputational geometry data structures dynamization intersection searching persistence
Unable to display preview. Download preview PDF.
- [AvK]P.K. Agarwal and M. van Kreveld. Connected component and simple polygon intersection searching. This Proceedings.Google Scholar
- [GJS92]P. Gupta, R. Janardan, and M. Smid. Further results on generalized intersection searching problems: counting, reporting, and dynamization. Technical Report TR-92-72, Dept. of Computer Science, University of Minnesota, 1992. Submitted.Google Scholar
- [JL93]R. Janardan and M. Lopez. Generalized intersection searching problems. International Journal of Computational Geometry & Applications, 3:39–69, 1993.Google Scholar
- [Lop91]M. Lopez. Algorithms for composite geometric objects. PhD thesis, Department of Computer Science, University of Minnesota, Minneapolis, Minnesota, 1991.Google Scholar
- [PS88]F.P. Preparata and M.I. Shamos. Computational Geometry — An Introduction. Springer-Verlag, 1988.Google Scholar