Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
Multidimensional divide-and-conquer
Communications of the ACM
A Sparse Table Implementation of Priority Queues
Proceedings of the 8th Colloquium on Automata, Languages and Programming
Two Simplified Algorithms for Maintaining Order in a List
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
New data structures for orthogonal range searching
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Optimal External Memory Interval Management
SIAM Journal on Computing
Compact representations of ordered sets
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Tight bounds for the partial-sums problem
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On dynamic range reporting in one dimension
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Space efficient dynamic orthogonal range reporting
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Fully Dynamic Orthogonal Range Reporting on RAM
SIAM Journal on Computing
Lower bounds for 2-dimensional range counting
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Universal codeword sets and representations of the integers
IEEE Transactions on Information Theory
Data Structures for Range Median Queries
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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In this paper we describe space-efficient data structures for two-dimensional range searching problem. We present a dynamic linear space data structure that supports orthogonal range reporting queries in O(log n + k logε n) time, where k is the size of the answer. Our data structure also supports emptiness and one-reporting queries in O(log n) time and thus achieves optimal time and space for this type of queries. In the case of integer point coordinates, we describe a static linear space data structure that supports range reporting queries in O(log n/log log n+k logε n) time and emptiness and one-reporting queries in O(log n/log log n) time. This is the first linear space data structure for these problems that achieves sub-logarithmic query time. We also present a dynamic linear space data structure for range counting queries with O((log n/ log log n)2) time and a dynamic O(n log n/ log log n) space data structure for semi-group range sum queries with query time O((log n/ log log n)2).