Space-efficient online computation of quantile summaries
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Fast incremental maintenance of approximate histograms
ACM Transactions on Database Systems (TODS)
Frequency Estimation of Internet Packet Streams with Limited Space
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Medians and beyond: new aggregation techniques for sensor networks
SenSys '04 Proceedings of the 2nd international conference on Embedded networked sensor systems
Tight lower bounds for selection in randomly ordered streams
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Robust lower bounds for communication and stream computation
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The average-case complexity of counting distinct elements
Proceedings of the 12th International Conference on Database Theory
Revisiting the Direct Sum Theorem and Space Lower Bounds in Random Order Streams
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Stream Order and Order Statistics: Quantile Estimation in Random-Order Streams
SIAM Journal on Computing
Streamed learning: one-pass SVMs
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
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We resolve the problem of small-space approximate selection in random-order streams. Specifically, we present an algorithm that reads the n elements of a set in random order and returns an element whose rank differs from the true median by at most n1/3+o(1) while storing a constant number of elements and counters at any one time. This is optimal: it was previously shown that achieving better accuracy required poly(n) memory. However, it was conjectured that the lower bound was not tight and that a previous algorithm achieving an n1/2+o(1) approximation was optimal. We therefore consider the new result a surprising resolution to a natural and basic question.