Private vs. common random bits in communication complexity
Information Processing Letters
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Data streams: algorithms and applications
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Estimating the sortedness of a data stream
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
On distance to monotonicity and longest increasing subsequence of a data stream
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Streaming computations with a loquacious prover
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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The deterministic space complexity of approximating the length of the longest increasing subsequence of a stream of N integers is known to be @Q@?(N). However, the randomized complexity is wide open. We show that the technique used in earlier work to establish the @W(N) deterministic lower bound fails strongly under randomization: specifically, we show that the communication problems on which the lower bound is based have very efficient randomized protocols. The purpose of this note is to guide and alert future researchers working on this very interesting problem.