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• W2988402777 abstract "We investigate adaptive sublinear algorithms for detecting monotone patterns in an array. Given fixed $2 leq k in mathbb{N}$ and $varepsilon > 0$, consider the problem of finding a length-$k$ increasing subsequence in an array $f colon [n] to mathbb{R}$, provided that $f$ is $varepsilon$-far from free of such subsequences. Recently, it was shown that the non-adaptive query complexity of the above task is $Theta((log n)^{lfloor log_2 k rfloor})$. In this work, we break the non-adaptive lower bound, presenting an adaptive algorithm for this problem which makes $O(log n)$ queries. This is optimal, matching the classical $Omega(log n)$ adaptive lower bound by Fischer [2004] for monotonicity testing (which corresponds to the case $k=2$), and implying in particular that the query complexity of testing whether the longest increasing subsequence (LIS) has constant length is $Theta(log n)$." @default.
• W2988402777 created "2019-11-22" @default.
• W2988402777 creator A5044142637 @default.
• W2988402777 creator A5048698980 @default.
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• W2988402777 date "2019-11-04" @default.
• W2988402777 modified "2023-09-23" @default.
• W2988402777 title "Optimal Adaptive Detection of Monotone Patterns" @default.
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• W2988402777 hasPublicationYear "2019" @default.
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