Making data structures persistent
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Approximate medians and other quantiles in one pass and with limited memory
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Maintaining Stream Statistics over Sliding Windows
SIAM Journal on Computing
Frequency Estimation of Internet Packet Streams with Limited Space
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
An Efficient Algorithm for the Approximate Median Selection Problem
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
Space-time tradeoff for answering range queries (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Continuously Maintaining Quantile Summaries of the Most Recent N Elements over a Data Stream
ICDE '04 Proceedings of the 20th International Conference on Data Engineering
Approximate counts and quantiles over sliding windows
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Journal of Computer and System Sciences
Range mode and range median queries on lists and trees
Nordic Journal of Computing
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
Range Quantile Queries: Another Virtue of Wavelet Trees
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
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
Cell probe lower bounds and approximations for range mode
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Range majority in constant time and linear space
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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
New algorithms on wavelet trees and applications to information retrieval
Theoretical Computer Science
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
Range majority in constant time and linear space
Information and Computation
Better space bounds for parameterized range majority and minority
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Data structures for range-aggregate extent queries
Computational Geometry: Theory and Applications
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We consider data structures and algorithms for preprocessing a labelled list of length n so that, for any given indices i and j we can answer queries of the form: What is the mode or median label in the sequence of labels between indices i and j. Our results are on approximate versions of this problem. Using $O(\frac{n}{1-\alpha})$ space, our data structure can find in $O({\rm log}{\rm log}_\frac{1}{\alpha} n)$ time an element whose number of occurrences is at least α times that of the mode, for some user-specified parameter 0αα=1/2,1/3 and 1/4, using storage space of O(n log n), O(n log log n) and O(n), respectively. Finally, if the elements are comparable, we construct an $O(\frac{n}{1-\alpha})$ space data structure that answers approximate range median queries. Specifically, given indices i and j, in O(1) time, an element whose rank is at least $\alpha \times \lfloor|j-i+1|/2\rfloor$ and at most $(2-\alpha)\times\lfloor|j-i+1|/2\rfloor$ is returned for 0α