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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 Theta~(sqrt N). However, the randomized complexity is wide open.
We show that the technique used in earlier work to establish the Omega(sqrt 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.
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
Or copy and paste:
Amit Chakrabarti, "A Note on Randomized Streaming Space Bounds for the Longest Increasing Subsequence Problem." Dartmouth Computer Science Technical Report TR2010-667, May 2010.
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