Algorithmica

, Volume 63, Issue 1–2, pp 457–475 | Cite as

External Memory Planar Point Location with Logarithmic Updates

  • Lars Arge
  • Gerth Stølting Brodal
  • S. Srinivasa Rao
Article
  • 153 Downloads

Abstract

Point location is an extremely well-studied problem both in internal memory models and recently also in the external memory model. In this paper, we present an I/O-efficient dynamic data structure for point location in general planar subdivisions. Our structure uses linear space to store a subdivision with N segments. Insertions and deletions of segments can be performed in amortized O(log  B N) I/Os and queries can be answered in \(O(\log_{B}^{2} N)\) I/Os in the worst-case. The previous best known linear space dynamic structure also answers queries in \(O(\log_{B}^{2} N)\) I/Os, but only supports insertions in amortized \(O(\log_{B}^{2} N)\) I/Os. Our structure is also considerably simpler than previous structures.

Keywords

Planar point location External memory model I/O model Vertical ray shooting query Dynamic data structure 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Lars Arge
    • 1
  • Gerth Stølting Brodal
    • 1
  • S. Srinivasa Rao
    • 2
  1. 1.MADALGO (Center for Massive Data Algorithmics—A Center of the Danish National Research Foundation), Department of Computer ScienceAarhus UniversityAarhus NDenmark
  2. 2.School of Computer Science and EngineeringSeoul National UniversitySeoulRepublic of Korea

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