The P2 algorithm for dynamic calculation of quantiles and histograms without storing observations
Communications of the ACM
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
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Space-efficient online computation of quantile summaries
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
A One-Pass Algorithm for Accurately Estimating Quantiles for Disk-Resident Data
VLDB '97 Proceedings of the 23rd International Conference on Very Large Data Bases
Frequency Estimation of Internet Packet Streams with Limited Space
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A simple algorithm for finding frequent elements in streams and bags
ACM Transactions on Database Systems (TODS)
ON LOWER BOUNDS FOR SELECTION PROBLEMS
ON LOWER BOUNDS FOR SELECTION PROBLEMS
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
Medians and beyond: new aggregation techniques for sensor networks
SenSys '04 Proceedings of the 2nd international conference on Embedded networked sensor systems
Approximate counts and quantiles over sliding windows
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Fast and approximate stream mining of quantiles and frequencies using graphics processors
Proceedings of the 2005 ACM SIGMOD international conference on Management of data
Approximate Processing of Massive Continuous Quantile Queries over High-Speed Data Streams
IEEE Transactions on Knowledge and Data Engineering
Approximate quantiles and the order of the stream
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A Fast Algorithm for Approximate Quantiles in High Speed Data Streams
SSDBM '07 Proceedings of the 19th International Conference on Scientific and Statistical Database Management
Continuously maintaining order statistics over data streams: extended abstract
ADC '07 Proceedings of the eighteenth conference on Australasian database - Volume 63
Quantiles over data streams: an experimental study
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
Mining frequent items in data stream using time fading model
Information Sciences: an International Journal
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This paper studies the space complexity of the ε-approximate quantiles problem, which asks for some data structure that enables us to determine, after reading a whole data stream, a φ-quantile (for any 0 ≤ φ ≤ 1) of the stream within some error bound ε. The best known algorithm for the problem uses O(1/ε log εN) words where N is the total number of items in the stream, or uses O(1/ε log |U|) words where U is the set of possible items. It is known that the space lower bound of the problem is Ω(1/ε) words; however, improvement of this bound is elusive. In this paper, we prove that any comparison-based algorithm for finding ε-approximate quantiles needs Ω(1/ε log 1/ε) words.