I/O-efficient map overlay and point location in low-density subdivisions

M. Berg, de, H.J. Haverkort, S. Thite, L. Toma

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

4 Citations (Scopus)
1 Downloads (Pure)

Abstract

We present improved and simplified -efficient algorithms for two problems on planar low-density subdivisions, namely map overlay and point location. More precisely, we show how to preprocess a low-density subdivision with n edges in i/o’s into a compressed linear quadtree such that one can: • compute the overlay of two preprocessed subdivisions in i/o’s, where n is the total number of edges in the two subdivisions, • answer a single point location query in O(log B n) i/o’s and k batched point location queries in i/o’s. For the special case where the subdivision is a fat triangulation, we show how to obtain the same bounds with an ordinary (uncompressed) quadtree, and we show how to make the structure fully dynamic using O(log B n) i/o’s per update. Our algorithms and data structures improve on the previous best known bounds for general subdivisions both in the number of i/o’s and storage usage, they are significantly simpler, and several of our algorithms are cache-oblivious.
Original languageEnglish
Title of host publicationProceedings of the 18th International Symposium : Algorithms and Computation (ISAAC 2007) 17-19 December 2007, Sendai, Japan
EditorsT. Takuyama
Place of PublicationBerlin
PublisherSpringer
Pages500-511
ISBN (Print)3-540-77118-2
DOIs
Publication statusPublished - 2007
Event18th International Symposium on Algorithms and Computation (ISAAC 2007) - Sendai, Japan
Duration: 17 Dec 200719 Dec 2007
Conference number: 18

Publication series

NameLecture Notes in Computer Science
Volume4835
ISSN (Print)0302-9743

Conference

Conference18th International Symposium on Algorithms and Computation (ISAAC 2007)
Abbreviated titleISAAC 2007
CountryJapan
CitySendai
Period17/12/0719/12/07

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