Random sampling with a reservoir
ACM Transactions on Mathematical Software (TOMS)
The P2 algorithm for dynamic calculation of quantiles and histograms without storing observations
Communications of the ACM
Selection from read-only memory and sorting with minimum data movement
Theoretical Computer Science
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
Space-efficient online computation of quantile summaries
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Streaming and sublinear approximation of entropy and information distances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximate quantiles and the order of the stream
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Journal of Computer and System Sciences
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In this paper the well-known problem of finding the median of an ordered set is studied under a very restrictive streaming model with sequential read-only access to the data. Only a constant number of reference objects from the stream can be stored for comparison with subsequent stream elements. A first non-trivial bound of $\Omega(\sqrt{n})$ distance to the extrema of the set is presented for a single pass over streams which do not reveal their total size n. For cases with known size, an algorithm is given which guarantees a distance of Ω(n1−ε) to the extrema, which is an ε-approximation for the proven best bound possible.