Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
Efficient 3-D range searching in external memory
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
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
Multidimensional divide-and-conquer
Communications of the ACM
New data structures for orthogonal range searching
FOCS '00 Proceedings of the 41st 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
A data structure for multi-dimensional range reporting
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Space Efficient Dynamic Orthogonal Range Reporting
Algorithmica
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Orthogonal range searching on the RAM, revisited
Proceedings of the twenty-seventh annual symposium on Computational geometry
Persistent predecessor search and orthogonal point location on the word RAM
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Succinct indices for range queries with applications to orthogonal range maxima
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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We present a data structure that supports three-dimensional range reporting queries in O (loglogU + (loglogn )3 + k ) time and uses O (n log1 + *** n ) space, where U is the size of the universe, k is the number of points in the answer, and *** is an arbitrary constant. This result improves over the data structure of Alstrup, Brodal, and Rauhe (FOCS 2000) that uses O (n log1 + *** n ) space and supports queries in O (logn + k ) time, the data structure of Nekrich (SoCG'07) that uses O (n log3 n ) space and supports queries in O (loglogU + (loglogn )2 + k ) time, and the data structure of Afshani (ESA'08) that uses O (n log3 n ) space and also supports queries in O (loglogU + (loglogn )2 + k ) time but relies on randomization during the preprocessing stage. Our result allows us to significantly reduce the space usage of the fastest previously known static and incremental d -dimensional data structures, d *** 3, at a cost of increasing the query time by a negligible O (loglogn ) factor.