Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
New data structures for orthogonal range queries
SIAM Journal on Computing
Filtering search: a new approach to query answering
SIAM Journal on Computing
Multidimensional search trees that provide new types of memory reductions
Journal of the ACM (JACM)
Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
Lower bounds for orthogonal range searching: part II. The arithmetic model
Journal of the ACM (JACM)
Applications of range query theory to relational data base join and selection operations
Journal of Computer and System Sciences
Design of Dynamic Data Structures
Design of Dynamic Data Structures
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A Sparse Table Implementation of Priority Queues
Proceedings of the 8th Colloquium on Automata, Languages and Programming
Cache-oblivious data structures for orthogonal range searching
Proceedings of the nineteenth annual symposium on Computational geometry
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
New data structures for orthogonal range searching
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Dynamic Algorithms in Computational Geometry
Dynamic Algorithms in Computational Geometry
A data structure for multi-dimensional range reporting
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Space-efficient dynamic orthogonal point location, segment intersection, and range reporting
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Orthogonal range searching in linear and almost-linear space
Computational Geometry: Theory and Applications
Orthogonal range searching in linear and almost-linear space
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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In this paper we present new space e cient dynamic data structures for orthogonal range reporting.The described data structures support planar range reporting queries in time O (log n +k log log(4 n/(k +1)))and space O (n log log n ), or in time O (log n+k )and space O (n log e n )for any e 0. Both data structures can be constructed in O (n log n )time and support insert and delete operations in amortized time O (log 2 n )and O (log n log log n )respectively. These results match the corresponding upper space bounds of Chazelle [6] for the static case. We also present a dynamic data structure for d -dimensional range reporting with search time O (log d .1 n +k ),update time O (log d n ),and space O (n log d .2+e n )for any e 0.