Efficient c-Oriented Range Searching with DOP-Trees

  • Mark de Berg
  • Herman Haverkort
  • Micha Streppel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)


A c-dop is a c-oriented convex polytope, that is, a convex polytope whose edges have orientations that come from a fixed set of c orientations. In this paper we study dop-trees—bounding-volume hierarchies that use c-dops as bounding volumes—in the plane. We prove that for any set S of n disjoint c-dops in the plane, one can construct a dop-tree such that a range query with a c-dop as query range can be answered in O(n 1/2 + ε  + k) time, where k is the number of reported answers. This is optimal up to the factor O(n ε ). If the c-dops in S may intersect, the query time becomes O(n \(^{\rm 1-1/{\it c}}\)+k), which is optimal.


Query Range Point Query Query Time Representative Point Splitting Line 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Mark de Berg
    • 1
  • Herman Haverkort
    • 1
  • Micha Streppel
    • 1
  1. 1.Department of Computer ScienceTU EindhovenEindhovenThe Netherlands

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