New data structures for orthogonal range queries
SIAM Journal on Computing
Adding range restriction capability to dynamic data structures
Journal of the ACM (JACM)
Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
High-order entropy-compressed text indexes
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Succinct Dynamic Data Structures
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Optimal External Memory Interval Management
SIAM Journal on Computing
Compressed representations of sequences and full-text indexes
ACM Transactions on Algorithms (TALG)
Lower bounds for 2-dimensional range counting
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Adaptive searching in succinctly encoded binary relations and tree-structured documents
Theoretical Computer Science
Rank and select revisited and extended
Theoretical Computer Science
Dynamic entropy-compressed sequences and full-text indexes
ACM Transactions on Algorithms (TALG)
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Orthogonal range searching in linear and almost-linear space
Computational Geometry: Theory and Applications
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
Rank/select on dynamic compressed sequences and applications
Theoretical Computer Science
Compressing and indexing labeled trees, with applications
Journal of the ACM (JACM)
Improved data structures for the orthogonal range successor problem
Computational Geometry: Theory and Applications
Succinct representations of dynamic strings
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Succinct indexes for strings, binary relations and multilabeled trees
ACM Transactions on Algorithms (TALG)
Space efficient data structures for dynamic orthogonal range counting
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Succinct Representation of Labeled Graphs
Algorithmica
Space-Efficient and fast algorithms for multidimensional dominance reporting and counting
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Dynamic range selection in linear space
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
The cell probe complexity of dynamic range counting
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We present a linear-space data structure that maintains a dynamic set of n points with coordinates of real numbers in the plane to support orthogonal range counting in O((lgnlglgn)^2) worst-case time, and insertions and deletions in O((lgnlglgn)^2) amortized time. This provides faster support for updates than previous results with the same bounds on space cost and query time. We also consider the same problem for points on a UxU grid, and design the first succinct data structure for a dynamic integer sequence, S, to support range counting queries defined as follows: Given a range, [i"1..i"2], of indices and a range, [v"1..v"2], of values, count the number of entries of S[i"1..i"2] that store integers from [v"1..v"2].