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    I/O-efficient dynamic point location in monotone planar subdivisions

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    Vitter_1999.pdf (1.222Mb)
    Issue Date
    1999
    Author
    Agarwal, Pankaj K.
    Arge, Lars
    Brodal, Gerth Stølting
    Vitter, Jeffrey Scott
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
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    Abstract
    We present an efficient external-memory dynamic data structure for point location in monotone planar subdivisions. Our data structure uses O(N/B) disk blocks to store a monotone subdivision of size N, where B is the size of a disk block. It supports queries in O(logi N) I/OS (worst-case) and updates in O(lo& N) I/OS (amortized). We also propose a new variant of B-trees, called leuelbalanced B-trees, which allow insert, delete, merge, and split operations in O((l+ $ logM,B f) log, N) I/OS (amortized), 2 5 b 2 B/2, even if each node stores a pointer to its parent. Here M is the size of main memory. Besides being essential to our point-location data structure, we believe that level-balanced B-trees are of significant independent interest. They can, for example, be used to dynamically maintain a planar St-graph using O((1 + $10g~,~ $$) log, N) = O(logi N) I/OS (amortized) per update, so that reachability queries can be answered in O(log, N) I/OS (worst case).
    URI
    http://hdl.handle.net/1808/7168
    DOI
    https://doi.org/10.1145/314500.314525
    Collections
    • Provost Office Published Articles [95]
    • Electrical Engineering and Computer Science Scholarly Works [288]
    • Distinguished Professors Scholarly Works [918]
    Citation
    P. K. Agarwal, L. Arge, G. Brodal, and J. S. Vitter. “I/O-Efficient Dynamic Point Location in Monotone Subdivisions,” Proceedings of the 10th Annual SIAM/ACM Symposium on Discrete Algorithms (SODA ’99), Baltimore, MD, January 1999, 11–20. http://doi.acm.org/10.1145/314500.314525

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    KU Libraries
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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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