The input/output complexity of sorting and related problems
Communications of the ACM
Modern database systems
Proceedings of the eleventh annual symposium on Computational geometry
Realistic input models for geometric algorithms
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Multidimensional access methods
ACM Computing Surveys (CSUR)
On two-dimensional indexability and optimal range search indexing
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Efficient searching with linear constraints
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Balanced aspect ratio trees: combining the advantages of k-d trees and octrees
Journal of Algorithms
External memory algorithms and data structures: dealing with massive data
ACM Computing Surveys (CSUR)
Box-trees for collision checking in industrial installations
Proceedings of the eighteenth annual symposium on Computational geometry
Design of Dynamic Data Structures
Design of Dynamic Data Structures
The K-D-B-tree: a search structure for large multidimensional dynamic indexes
SIGMOD '81 Proceedings of the 1981 ACM SIGMOD international conference on Management of data
External memory data structures
Handbook of massive data sets
Balanced aspect ratio trees
Guarding scenes against invasive hypercubes
Computational Geometry: Theory and Applications
The Priority R-tree: a practically efficient and worst-case optimal R-tree
SIGMOD '04 Proceedings of the 2004 ACM SIGMOD international conference on Management of data
R-Trees: Theory and Applications (Advanced Information and Knowledge Processing)
R-Trees: Theory and Applications (Advanced Information and Knowledge Processing)
Approximate range searching using binary space partitions
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
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In this paper, we present two linear-size external memory data structures for approximate range searching. Our first structure, the BAR-B-tree, stores a set of N points in Rd and can report all points inside a query range Q by accessing O(logB N + Ɛγ + kƐ/B) disk blocks, where B is the disk block size, γ = 1 - d for convex queries and γ = -d otherwise, and kƐ is the number of points lying within a distance of Ɛ ċdiam(Q) to the query range Q. Our second structure, the object-BARB-tree, is able to store objects of arbitrary shapes of constant complexity and provides similar query guarantees. In addition, both structures also support other types of range searching queries such as range aggregation and nearest-neighbor. Finally, we present I/O-efficient algorithms to build these structures.