All reports by Author Ramesh Krishnan S. Pallavoor:

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TR19-163
| 16th November 2019
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Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, Erik Waingarten#### Approximating the Distance to Monotonicity of Boolean Functions

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TR17-111
| 2nd June 2017
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Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, C. Seshadhri#### A Lower Bound for Nonadaptive, One-Sided Error Testing of Unateness of Boolean Functions over the Hypercube

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TR17-103
| 12th June 2017
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Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, Nithin Varma#### Parameterized Property Testing of Functions

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TR17-049
| 14th March 2017
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Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, C. Seshadhri#### Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps

Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, Erik Waingarten

We design a nonadaptive algorithm that, given a Boolean function $f\colon \{0,1\}^n \to \{0,1\}$ which is $\alpha$-far from monotone, makes poly$(n, 1/\alpha)$ queries and returns an estimate that, with high probability, is an $\widetilde{O}(\sqrt{n})$-approximation to the distance of $f$ to monotonicity. Furthermore, we show that for any constant $\kappa > ... more >>>

Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, C. Seshadhri

A Boolean function $f:\{0,1\}^d \to \{0,1\}$ is unate if, along each coordinate, the function is either nondecreasing or nonincreasing. In this note, we prove that any nonadaptive, one-sided error unateness tester must make $\Omega(\frac{d}{\log d})$ queries. This result improves upon the $\Omega(\frac{d}{\log^2 d})$ lower bound for the same class of ... more >>>

Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, Nithin Varma

We investigate the parameters in terms of which the complexity of sublinear-time algorithms should be expressed. Our goal is to find input parameters that are tailored to the combinatorics of the specific problem being studied and design algorithms that run faster when these parameters are small. This direction enables us ... more >>>

Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, C. Seshadhri

We study the problem of testing unateness of functions $f:\{0,1\}^d \to \mathbb{R}.$ We give a $O(\frac{d}{\epsilon} \cdot \log\frac{d}{\epsilon})$-query nonadaptive tester and a $O(\frac{d}{\epsilon})$-query adaptive tester and show that both testers are optimal for a fixed distance parameter $\epsilon$. Previously known unateness testers worked only for Boolean functions, and their query ... more >>>