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Further results on generalized intersection searching problems: Counting, reporting, and dynamization

  • Prosenjit Gupta
  • Ravi Janardan
  • Michiel Smid
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 709)

Abstract

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.

Keywords

Computational geometry data structures dynamization intersection searching persistence 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Prosenjit Gupta
    • 1
  • Ravi Janardan
    • 1
  • Michiel Smid
    • 2
  1. 1.Department of Computer ScienceUniversity of MinnesotaMinneapolisUSA
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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