SIAM Journal on Computing
Merging multiple lists on hierarchical-memory multiprocessors
Journal of Parallel and Distributed Computing - Special issue on shared-memory multiprocessors
Computing 2-D Min, Median, and Max Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Binary search trees of bounded balance
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
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
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Range mode and range median queries in constant time and sub-quadratic space
Information Processing Letters
Orthogonal range searching in linear and almost-linear space
Computational Geometry: Theory and Applications
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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
Space-Efficient and fast algorithms for multidimensional dominance reporting and counting
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Median Filtering in Constant Time
IEEE Transactions on Image Processing
Colored range queries and document retrieval
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Beyond simple aggregates: indexing for summary queries
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
New algorithms on wavelet trees and applications to information retrieval
Theoretical Computer Science
Path queries in weighted trees
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Dynamic range selection in linear space
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Linear-Space data structures for range minority query in arrays
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Succinct data structures for path queries
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Colored range queries and document retrieval
Theoretical Computer Science
Indexing for summary queries: Theory and practice
ACM Transactions on Database Systems (TODS)
Spaces, Trees, and Colors: The algorithmic landscape of document retrieval on sequences
ACM Computing Surveys (CSUR)
Compact binary relation representations with rich functionality
Information and Computation
| Hi-index | 5.23 |
We consider the following problem: Given an unsorted array of n elements, and a sequence of intervals in the array, compute the median in each of the subarrays defined by the intervals. We describe a simple algorithm which needs O(nlogk+klogn) time to answer k such median queries. This improves previous algorithms by a logarithmic factor and matches a comparison lower bound for k=O(n). The space complexity of our simple algorithm is O(nlogn) in the pointer machine model, and O(n) in the RAM model. In the latter model, a more involved O(n) space data structure can be constructed in O(nlogn) time where the time per query is reduced to O(logn/loglogn). We also give efficient dynamic variants of both data structures, achieving O(log^2n) query time using O(nlogn) space in the comparison model and O((logn/loglogn)^2) query time using O(nlogn/loglogn) space in the RAM model, and show that in the cell-probe model, any data structure which supports updates in O(log^O^(^1^)n) time must have @W(logn/loglogn) query time. Our approach naturally generalizes to higher-dimensional range median problems, where element positions and query ranges are multidimensional-it reduces a range median query to a logarithmic number of range counting queries.