Introduction to Algorithms
Computing 2-D Min, Median, and Max Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Succinct Dynamic Data Structures
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Optimal External Memory Interval Management
SIAM Journal on Computing
Range mode and range median queries on lists and trees
Nordic Journal of Computing
Lower bounds for 2-dimensional range counting
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Range mode and range median queries in constant time and sub-quadratic space
Information Processing Letters
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Range Quantile Queries: Another Virtue of Wavelet Trees
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
Data Structures for Range Median Queries
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Improved bounds for range mode and range median queries
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Succinct representations of dynamic strings
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Theoretical Computer Science
Space efficient data structures for dynamic orthogonal range counting
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Range selection and median: tight cell probe lower bounds and adaptive data structures
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximate range mode and range median queries
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Space efficient data structures for dynamic orthogonal range counting
Computational Geometry: Theory and Applications
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Given a set S of n points in the plane, we consider the problem of answering range selection queries on S: that is, given an arbitrary x-range Q and an integer k0, return the k-th smallest y-coordinate from the set of points that have x-coordinates in Q. We present a linear space data structure that maintains a dynamic set of n points in the plane with real coordinates, and supports range selection queries in $O((\lg n / \lg \lg n)^2)$ time, as well as insertions and deletions in $O((\lg n / \lg \lg n)^2)$ amortized time. The space usage of this data structure is an $\Theta(\lg n / \lg \lg n)$ factor improvement over the previous best result, while maintaining asymptotically matching query and update times. We also present a succinct data structure that supports range selection queries on a dynamic array of n values drawn from a bounded universe.