Searching for segments with largest relative overlap

  • Franz Aurenhammer
  • Gerd Stöckl
II Mathematical Programming Algorithms II.1 Computational Geometry
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)


Let S be a set of n possibly intersecting line segments on the x-axis. A data structure is developed that — for an arbitrary query segment σ — reports in O(log n) time a segment in S which yields the largest relative overlap with σ. The structure needs O(n log n) time and O(n) space for construction. These bounds are asymptotically optimal.


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Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • Franz Aurenhammer
    • 1
  • Gerd Stöckl
    • 2
  1. 1.Institut für Informatik, Fachbereich MathematikFreie Universität BerlinBerlin 33Germany
  2. 2.Institute für InformationsverarbeitungTechnische Universität GrazGrazAustria

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