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External Memory Planar Point Location with Logarithmic Updates

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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.

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Authors and Affiliations

  1. MADALGO (Center for Massive Data Algorithmics—A Center of the Danish National Research Foundation), Department of Computer Science, Aarhus University, IT Parken, Aabogade 34, 8200, Aarhus N, Denmark

    Lars Arge & Gerth Stølting Brodal

  2. School of Computer Science and Engineering, Seoul National University, 599 Gwanakro, Gwanak-Gu, Seoul, 151-744, Republic of Korea

    S. Srinivasa Rao

Authors
  1. Lars Arge
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  2. Gerth Stølting Brodal
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  3. S. Srinivasa Rao
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Corresponding author

Correspondence to S. Srinivasa Rao.

Additional information

L. Arge was supported in part by the US Army Research Office through grant W911NF-04-01-0278, by an Ole Roemer Scholarship from the Danish National Science Research Council, a NABIIT grant from the Danish Strategic Research Council, and by the Danish National Research Foundation.

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Arge, L., Brodal, G.S. & Rao, S.S. External Memory Planar Point Location with Logarithmic Updates. Algorithmica 63, 457–475 (2012). https://doi.org/10.1007/s00453-011-9541-2

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