Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
Algorithms for three-dimensional dominance searching in linear space
Information Processing Letters
Exponential Structures for Efficient Cache-Oblivious Algorithms
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Handbook Of Data Structures And Applications (Chapman & Hall/Crc Computer and Information Science Series.)
Succinct indexes for strings, binary relations and multi-labeled trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Orthogonal range searching in linear and almost-linear space
Computational Geometry: Theory and Applications
Succinct geometric indexes supporting point location queries
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Space Efficient Multi-dimensional Range Reporting
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Succinct Orthogonal Range Search Structures on a Grid with Applications to Text Indexing
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Transdichotomous Results in Computational Geometry, I: Point Location in Sublogarithmic Time
SIAM Journal on Computing
Data Structures for Range Median Queries
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Proceedings of the twenty-sixth annual symposium on Computational geometry
Data structures for range minimum queries in multidimensional arrays
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On space efficient two dimensional range minimum data structures
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Orthogonal range searching on the RAM, revisited
Proceedings of the twenty-seventh annual symposium on Computational geometry
Space-Efficient and fast algorithms for multidimensional dominance reporting and counting
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Encoding 2d range maximum queries
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Two dimensional range minimum queries and fibonacci lattices
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We consider the problem of preprocessing N points in 2D, each endowed with a priority, to answer the following queries: given a axis-parallel rectangle, determine the point with the largest priority in the rectangle. Using the ideas of the effective entropy of range maxima queries and succinct indices for range maxima queries, we obtain a structure that uses O(N) words and answers the above query in O(logN loglogN) time. This a direct improvement of Chazelle's result from 1985 [10] for this problem --- Chazelle required O(N/ε) words to answer queries in O((logN)1+ε) time for any constant ε0.