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The Cartographer
Adaptive Boolean Monotonicity Testing in Total Influence Time
January 09, 2018 Β· Declared Dead Β· π Electron. Colloquium Comput. Complex.
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Authors
Deeparnab Chakrabarty, C. Seshadhri
arXiv ID
1801.02816
Category
cs.DS: Data Structures & Algorithms
Cross-listed
cs.CC,
cs.DM
Citations
14
Venue
Electron. Colloquium Comput. Complex.
Last Checked
3 months ago
Abstract
The problem of testing monotonicity of a Boolean function $f:\{0,1\}^n \to \{0,1\}$ has received much attention recently. Denoting the proximity parameter by $\varepsilon$, the best tester is the non-adaptive $\widetilde{O}(\sqrt{n}/\varepsilon^2)$ tester of Khot-Minzer-Safra (FOCS 2015). Let $I(f)$ denote the total influence of $f$. We give an adaptive tester whose running time is $I(f)poly(\varepsilon^{-1}\log n)$.
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