The input/output complexity of sorting and related problems
Communications of the ACM
Two- and three-dimensional point location in rectangular subdivisions
Journal of Algorithms
Dynamic rectangular point location, with an application to the closest pair problem
Information and Computation
Efficient 3-D range searching in external memory
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Handbook of discrete and computational geometry
The P-range tree: a new data structure for range searching in secondary memory
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
I/O-efficient dynamic point location in monotone planar subdivisions
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Theory and practice of I/O-efficient algorithms for multidimensional batched searching problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
External memory algorithms and data structures: dealing with massive data
ACM Computing Surveys (CSUR)
Exponential Structures for Efficient Cache-Oblivious Algorithms
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
I/O-efficient dynamic planar point location
Computational Geometry: Theory and Applications
An optimal dynamic interval stabbing-max data structure?
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Time-space trade-offs for predecessor search
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A data structure for multi-dimensional range reporting
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
External-memory computational geometry
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
External memory range reporting on a grid
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
I/O-efficient data structures for colored range and prefix reporting
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Persistent predecessor search and orthogonal point location on the word RAM
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
External memory orthogonal range reporting with fast updates
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Computing discriminating and generic words
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
Persistent Predecessor Search and Orthogonal Point Location on the Word RAM
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
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In this paper we present an external memory data structure for point location queries in a set of d-dimensional rectangles. Our data structure uses O(N/B) blocks of space and supports point location queries in O(logBd-1 N) I/Os, where N is the number of rectangles and B is the block size. We also present a O((N/B) logB N) space data structure that supports point location queries in a two-dimensional rectangular subdivision of a U×U grid in O(log2 logB U+(log2 logB N)2) I/Os and a O((N/B) logB2 N) space data structure that supports point location queries in a three-dimensional rectangular subdivision in O(logB N) I/Os. As an application of our result, we describe a data structure for three-dimensional orthogonal range reporting queries on a grid of size U with O(log2 logB U + (log2 logB N)2 + T/B) I/O operations per query, where T is the number of points in the answer.