article

Box-Trees and R-Trees with Near-Optimal Query Time

Authors:

H. J. HaverkortAuthors Info & Claims

Discrete & Computational Geometry, Volume 28, Issue 3

Pages 291 - 312

https://doi.org/10.1007/s00454-002-2817-1

Published: 01 August 2002 Publication History

Abstract

A box-tree is a bounding-volume hierarchy that uses axis-aligned boxes as bounding volumes. The query complexity of a box-tree with respect to a given type of query is the maximum number of nodes visited when answering such a query. We describe several new algorithms for constructing box-trees with small worst-case query complexity with respect to queries with axis-parallel boxes and with points. We also prove lower bounds on the worst-case query complexity for box-trees, which show that our results are optimal or close to optimal. Finally, we present algorithms to convert box-trees to R-trees, resulting in R-trees with (almost) optimal query complexity.

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Cited By

Yang JCong G(2023)PLATON: Top-down R-tree Packing with Learned Partition PolicyProceedings of the ACM on Management of Data10.1145/36267421:4(1-26)Online publication date: 12-Dec-2023
https://dl.acm.org/doi/10.1145/3626742
Hema TEaswarakumar KAkila VSivakumar NSaruladha KZayaraz GIlavarasan E(2016)On Higher Dimensional Window QueryProceedings of the International Conference on Informatics and Analytics10.1145/2980258.2980448(1-6)Online publication date: 25-Aug-2016
https://dl.acm.org/doi/10.1145/2980258.2980448
Agarwal PFox KMunagala KNath AMilo TTan W(2016)Parallel Algorithms for Constructing Range and Nearest-Neighbor Searching Data StructuresProceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/2902251.2902303(429-440)Online publication date: 15-Jun-2016
https://dl.acm.org/doi/10.1145/2902251.2902303
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Box-Trees and R-Trees with Near-Optimal Query Time
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation

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Published In

cover image Discrete & Computational Geometry

Discrete & Computational Geometry Volume 28, Issue 3

August 2002

153 pages

ISSN:0179-5376

Issue’s Table of Contents

Copyright © Copyright © 2002 Springer-Verlag New York Inc.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 August 2002

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Cited By

Yang JCong G(2023)PLATON: Top-down R-tree Packing with Learned Partition PolicyProceedings of the ACM on Management of Data10.1145/36267421:4(1-26)Online publication date: 12-Dec-2023
https://dl.acm.org/doi/10.1145/3626742
Hema TEaswarakumar KAkila VSivakumar NSaruladha KZayaraz GIlavarasan E(2016)On Higher Dimensional Window QueryProceedings of the International Conference on Informatics and Analytics10.1145/2980258.2980448(1-6)Online publication date: 25-Aug-2016
https://dl.acm.org/doi/10.1145/2980258.2980448
Agarwal PFox KMunagala KNath AMilo TTan W(2016)Parallel Algorithms for Constructing Range and Nearest-Neighbor Searching Data StructuresProceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/2902251.2902303(429-440)Online publication date: 15-Jun-2016
https://dl.acm.org/doi/10.1145/2902251.2902303
Chen XLin YWang CShen GWang X(2012)A virtual training system using a force feedback haptic device for oral implantologyTransactions on Edutainment VIII10.5555/2363273.2363296(232-240)Online publication date: 1-Jan-2012
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Yi K(2012)The priority R-treeSIGSPATIAL Special10.1145/2367574.23675764:2(8-12)Online publication date: 1-Jul-2012
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Streppel MYi K(2011)Approximate Range Searching in External MemoryAlgorithmica10.5555/3118734.311882559:2(115-128)Online publication date: 1-Feb-2011
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Yang YPapadopoulos SPapadias DKollios G(2009)Authenticated indexing for outsourced spatial databasesThe VLDB Journal — The International Journal on Very Large Data Bases10.5555/1553321.155332818:3(631-648)Online publication date: 1-Jun-2009
https://dl.acm.org/doi/10.5555/1553321.1553328
de Berg MHaverkort HStreppel M(2009)Efficient c-oriented range searching with DOP-treesComputational Geometry: Theory and Applications10.1016/j.comgeo.2008.05.00242:3(250-267)Online publication date: 1-Apr-2009
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Arge LBerg MHaverkort H(2009)Cache-Oblivious R-TreesAlgorithmica10.1007/s00453-007-9007-853:1(50-68)Online publication date: 1-Jan-2009
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Berg MHachenberger P(2009)Rotated-Box TreesProceedings of the 8th International Symposium on Experimental Algorithms10.1007/978-3-642-02011-7_8(63-75)Online publication date: 4-Jun-2009
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