Dynamic 3-Sided Planar Range Queries with Expected Doubly Logarithmic Time

  • Gerth Stølting Brodal
  • Alexis C. Kaporis
  • Spyros Sioutas
  • Konstantinos Tsakalidis
  • Kostas Tsichlas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)


We consider the problem of maintaining dynamically a set of points in the plane and supporting range queries of the type [a,b]×( − ∞ , c]. We assume that the inserted points have their x-coordinates drawn from a class of smooth distributions, whereas the y-coordinates are arbitrarily distributed. The points to be deleted are selected uniformly at random among the inserted points. For the RAM model, we present a linear space data structure that supports queries in O(loglogn + t) expected time with high probability and updates in O(loglogn) expected amortized time, where n is the number of points stored and t is the size of the output of the query. For the I/O model we support queries in O(loglog B n + t/B) expected I/Os with high probability and updates in O(log B logn) expected amortized I/Os using linear space, where B is the disk block size. The data structures are deterministic and the expectation is with respect to the input distribution.


Range Query Query Time Smooth Distribution Lower Common Ancestor Empty Slot 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gerth Stølting Brodal
    • 1
  • Alexis C. Kaporis
    • 2
  • Spyros Sioutas
    • 3
  • Konstantinos Tsakalidis
    • 1
  • Kostas Tsichlas
    • 4
  1. 1.MADALGO, Department of Computer ScienceAarhus UniversityDenmark
  2. 2.Computer Engineering and Informatics DepartmentUniversity of PatrasGreece
  3. 3.Department of InformaticsIonian UniversityCorfuGreece
  4. 4.Department of InformaticsAristotle University of ThessalonikiGreece

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