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

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2007.54

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.

INDEX TERMS

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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

CITATIONS