New trie data structures which support very fast search operations
Journal of Computer and System Sciences
A log log n data structure for three-sided range queries
Information Processing Letters
Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
The input/output complexity of sorting and related problems
Communications of the ACM
Efficient data structures for range searching on a grid
Journal of Algorithms
Priority search trees in secondary memory (extended abstract)
Proceedings of the International Workshop WG '87 on Graph-theoretic concepts in computer science
Path caching (extended abstract): a technique for optimal external searching
PODS '94 Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Two- and three-dimensional point location in rectangular subdivisions
Journal of Algorithms
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
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
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
Efficient splitting and merging algorithms for order decomposable problems
Information and Computation
External memory algorithms and data structures: dealing with massive data
ACM Computing Surveys (CSUR)
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
New data structures for orthogonal range searching
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Faster deterministic sorting and searching in linear space
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Time-space trade-offs for predecessor search
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Planar Point Location in Sublogarithmic Time
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
A data structure for multi-dimensional range reporting
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
I/O-efficient point location in a set of rectangles
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
I/O-efficient data structures for colored range and prefix reporting
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Top-K color queries for document retrieval
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Space-efficient range reporting for categorical data
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Efficient range searching for categorical and plain data
ACM Transactions on Database Systems (TODS)
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In this paper we present external memory data structures for orthogonal range reporting queries on a grid. Our data structure for twodimensional orthogonal range reporting queries uses O((N/B) log2 N) blocks of space of size B and supports queries in optimal O(log2 logB U+ T/B) time, where U is the size of universe, N is the number of elements in the data structure, and T is the size of the answer. Our data structure for three-sided range reporting queries that uses O(N/B) blocks of space and supports queries in O(log2 logB U +T/B) time. In the case of threesided range reporting on a N × N grid, we describe a O((N/B) logB2 N) space data structure with O(T/B) query time, a O((N/B) logB* N) data structure with O(logB* N + T/B) query time, and a O(N/B) space data structure with O(logB(k) N + T/B) query time for any constant k.