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Point Location in Incremental Planar Subdivisions

Author Eunjin Oh

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Eunjin Oh
  • Max Planck Institute for Informatics, Saarbrücken, Germany

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Eunjin Oh. Point Location in Incremental Planar Subdivisions. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 51:1-51:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


We study the point location problem in incremental (possibly disconnected) planar subdivisions, that is, dynamic subdivisions allowing insertions of edges and vertices only. Specifically, we present an O(n log n)-space data structure for this problem that supports queries in O(log^2 n) time and updates in O(log n log log n) amortized time. This is the first result that achieves polylogarithmic query and update times simultaneously in incremental planar subdivisions. Its update time is significantly faster than the update time of the best known data structure for fully-dynamic (possibly disconnected) planar subdivisions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Dynamic point location
  • general incremental planar subdivisions


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