Dynamic Planar Point Location in External Memory

Authors J. Ian Munro, Yakov Nekrich

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J. Ian Munro
  • Cheriton School of Computer Science, University of Waterloo, Canada
Yakov Nekrich
  • Cheriton School of Computer Science, University of Waterloo, Canada

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J. Ian Munro and Yakov Nekrich. Dynamic Planar Point Location in External Memory. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


In this paper we describe a fully-dynamic data structure for the planar point location problem in the external memory model. Our data structure supports queries in O(log_B n(log log_B n)^3)) I/Os and updates in O(log_B n(log log_B n)^2)) amortized I/Os, where n is the number of segments in the subdivision and B is the block size. This is the first dynamic data structure with almost-optimal query cost. For comparison all previously known results for this problem require O(log_B^2 n) I/Os to answer queries. Our result almost matches the best known upper bound in the internal-memory model.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Theory of computation
  • Data Structures
  • Dynamic Data Structures
  • Planar Point Location
  • External Memory


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