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48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) (2007)
Providence, Rhode Island
Oct. 21, 2007 to Oct. 23, 2007
ISSN: 0272-5428
ISBN: 0-7695-3010-9
pp: 294-304
ABSTRACT
We show that any deterministic data-stream algorithm that makes a constant number of passes over the input and gives a constant factor approximation of the length of the longest increasing subsequence in a sequence of length n must use space \Omega \left( {\sqrt n } \right). This proves a conjecture made by Gopalan, Jayram, Krauthgamer and Kumar [10] who proved a matching upper bound. Our results yield asymptotically tight lower bounds for all approximation factors, thus resolving the main open problem from their paper. Our proof is based on analyzing a related communication problem and proving a direct sum type property for it.
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CITATION

A. Gál and P. Gopalan, "Lower Bounds on Streaming Algorithms for Approximating the Length of the Longest Increasing Subsequence," 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)(FOCS), Providence, Rhode Island, 2007, pp. 294-304.
doi:10.1109/FOCS.2007.54
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