article

Linear space data structures for two types of range search

Authors:

Bernard Chazelle,

Herbert EdelsbrunnerAuthors Info & Claims

Discrete & Computational Geometry, Volume 2, Issue 2

Pages 113 - 126

https://doi.org/10.1007/BF02187875

Published: 01 December 1987 Publication History

Abstract

This paper investigates the existence of linear space data structures for range searching. We examine thehomothetic range search problem, where a setS ofn points in the plane is to be preprocessed so that for any triangleT with sides parallel to three fixed directions the points ofS that lie inT can be computed efficiently. We also look atdomination searching in three dimensions. In this problem,S is a set ofn points inE3 and the question is to retrieve all points ofS that are dominated by some query point. We describe linear space data structures for both problems. The query time is optimal in the first case and nearly optimal in the second.

References

[1]

J. L. Bentley, Multidimensional divide and conquer,Comm. ACM23 (1980), 214---229.

[2]

B. Chazelle, Filtering search: a new approach to query-answering,SIAM J. Comput.15 (1986), 703---724.

Digital Library

[3]

B. Chazelle, A Functional Approach to Data Structures and Its Use in Multidimensional Searching, Technical Report No. CS-85-16, Brown University, 1985. Preliminary version inProceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science, 165---174, 1985.

[4]

B. Chazelle, Lower bounds on the complexity of multidimensional searching,Proceedings of the 27th Annual IEEE Symposium on Foundations of Computer Science, 87---96, 1986.

[5]

B. Chazelle and H. Edelsbrunner, Optimal solutions for a class of point retrieval problems,J. Symbolic Comput.1 (1985), 47---56.

Digital Library

[6]

B. Chazelle and L. J. Guibas, Fractional cascading: I. A data structuring technique,Algorithmica1 (1986), 133---162.

[7]

B. Chazelle, L. J. Guibas, and D. T. Lee, The power of geometric duality,Proceedings of the 24th Annual IEEE Symposium on Foundations of Computer Science, 217---225, 1983. Also inBIT25 (1985), 76---90.

[8]

D. P. Dobkin and H. Edelsbrunner, Space searching for interesting objects,Proceedings of the 25th Annual IEEE Symposium on Foundations of Computer Science, 387---392, 1984.

[9]

H. Edelsbrunner and E. Welzl, Halfplanar range search in linear space andO(n0.695) query time,Inform. Process. Lett., to appear.

[10]

H. Edelsbrunner, L. J. Guibas, and J. Stolfi, Optimal point location in a monotone subdivision,SIAM J. Comput.15 (1986), 317---340.

Digital Library

[11]

H. N. Gabow, J. L. Bentley, and R. E. Tarjan, Scaling and related techniques for geometry problems,Proceedings of the 16th Annual ACM Symposium on Theory of Computation, 135---143, 1984.

[12]

L. J. Guibas and J. Stolfi, Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams,ACM Trans. Graphics4 (1985), 74---123.

[13]

D. G. Kirkpatrick, Optimal search in planar subdivisions,SIAM J. Comput.12 (1983), 28---35.

[14]

H. T. Kung, F. Luccio, and F. P. Preparata, On finding the maxima of a set of vectors,J. Assoc. Comput. Mach.22 (1975), 469---476.

Digital Library

[15]

R. J. Lipton and R. E. Tarjan, Applications of a planar separator theorem,SIAM J. Comput.9 (1980), 615---627.

[16]

E. M. McCreight, Priority search trees,SIAM. J. Comput.14 (1985), 257---276.

[17]

D. E. Muller and F. P. Preparata, Finding the intersection of two convex polyhedra,Theoret. Comput. Sci.7 (1978), 217---236.

[18]

D. E. Willard, Polygon retrieval,SIAM J. Comput.11 (1982), 149---165.

[19]

F. F. Yao, A 3-space partition and its applications,Proceedings of the 15th Annual ACM Symposium on Theory of Computing, 258---263, 1983.

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Akram WSaxena S(2023)Point Enclosure Problem for Homothetic PolygonsCombinatorial Algorithms10.1007/978-3-031-34347-6_2(13-24)Online publication date: 7-Jun-2023
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Rahul STao Y(2022)Generic Techniques for Building Top-k StructuresACM Transactions on Algorithms10.1145/354607418:4(1-23)Online publication date: 10-Oct-2022
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Published In

cover image Discrete & Computational Geometry

Discrete & Computational Geometry Volume 2, Issue 2

June 1987

123 pages

ISSN:0179-5376

Issue’s Table of Contents

Copyright © Copyright © 1987 Springer-Verlag New York Inc.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 1987

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Cited By

Akram WSaxena S(2024)Dominance for Enclosure ProblemsCombinatorial Algorithms10.1007/978-3-031-63021-7_31(408-420)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-63021-7_31
Akram WSaxena S(2023)Point Enclosure Problem for Homothetic PolygonsCombinatorial Algorithms10.1007/978-3-031-34347-6_2(13-24)Online publication date: 7-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-34347-6_2
Rahul STao Y(2022)Generic Techniques for Building Top-k StructuresACM Transactions on Algorithms10.1145/354607418:4(1-23)Online publication date: 10-Oct-2022
https://dl.acm.org/doi/10.1145/3546074
Nekrich YMarx D(2021)New data structures for orthogonal range reporting and range minima queriesProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458137(1191-1205)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458137
Chan TNekrich YSmid M(2019)Orthogonal Range Reporting and Rectangle Stabbing for Fat RectanglesAlgorithms and Data Structures10.1007/978-3-030-24766-9_21(283-295)Online publication date: 5-Aug-2019
https://dl.acm.org/doi/10.1007/978-3-030-24766-9_21
Afshani PBerg MCasanova HKarsin BLambrechts CSitchinava NTsirogiannis C(2018)An Efficient Algorithm for the 1D Total Visibility-Index Problem and Its ParallelizationACM Journal of Experimental Algorithmics10.1145/320968523(1-23)Online publication date: 18-Jul-2018
https://dl.acm.org/doi/10.1145/3209685
Patil MThankachan SShah RNekrich YVitter JHull RGrohe M(2014)Categorical range maxima queriesProceedings of the 33rd ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems10.1145/2594538.2594557(266-277)Online publication date: 18-Jun-2014
https://dl.acm.org/doi/10.1145/2594538.2594557
Karpinski MNekrich Y(2009)Space Efficient Multi-dimensional Range ReportingProceedings of the 15th Annual International Conference on Computing and Combinatorics10.1007/978-3-642-02882-3_22(215-224)Online publication date: 11-Jul-2009
https://dl.acm.org/doi/10.1007/978-3-642-02882-3_22
Vitter J(2008)Algorithms and data structures for external memoryFoundations and Trends® in Theoretical Computer Science10.1561/04000000142:4(305-474)Online publication date: 1-Jan-2008
https://dl.acm.org/doi/10.1561/0400000014
JaJa JMortensen CShi Q(2004)Space-Efficient and Fast Algorithms for Multidimensional Dominance Reporting and CountingAlgorithms and Computation10.1007/978-3-540-30551-4_49(558-568)Online publication date: 20-Dec-2004
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