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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > ISOPERIMETRIC INEQUALITIES:
Reports tagged with Isoperimetric inequalities:
TR20-174 | 18th November 2020
Hadley Black, Iden Kalemaj, Sofya Raskhodnikova

Isoperimetric Inequalities for Real-Valued Functions with Applications to Monotonicity Testing

We generalize the celebrated isoperimetric inequality of Khot, Minzer, and Safra (SICOMP 2018) for Boolean functions to the case of real-valued functions $f \colon \{0,1\}^d\to\mathbb{R}$. Our main tool in the proof of the generalized inequality is a new Boolean decomposition that represents every real-valued function $f$ over an arbitrary partially ... more >>>




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