Dynamic Planar Point Location in External Memory

J. Ian Munro; Yakov Nekrich

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arXiv · 1903.06601

Dynamic Planar Point Location in External Memory

J. Ian Munro·Yakov Nekrich

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Abstract

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.

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BibTeX RIS

J. Ian Munro, Yakov Nekrich. 2019-03-15. Dynamic Planar Point Location in External Memory. https://arxiv.org/abs/1903.06601

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