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Electronic Colloquium on Computational Complexity

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All reports by Author Deeparnab Chakrabarty:

TR18-005 | 9th January 2018
C. Seshadhri, Deeparnab Chakrabarty

Adaptive Boolean Monotonicity Testing in Total Influence Time

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 ... more >>>

TR17-159 | 28th October 2017
Hadley Black, Deeparnab Chakrabarty, C. Seshadhri

A $o(d) \cdot \text{polylog}~n$ Monotonicity Tester for Boolean Functions over the Hypergrid $[n]^d$

We study monotonicity testing of Boolean functions over the hypergrid $[n]^d$ and design a non-adaptive tester with $1$-sided error whose query complexity is $\tilde{O}(d^{5/6})\cdot \text{poly}(\log n,1/\epsilon)$. Previous to our work, the best known testers had query complexity linear in $d$ but independent of $n$. We improve upon these testers as ... more >>>

TR17-111 | 2nd June 2017
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

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 >>>

TR17-049 | 14th March 2017
Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, C. Seshadhri

Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps

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 >>>

TR16-133 | 25th August 2016
C. Seshadhri, Deeparnab Chakrabarty

A $\widetilde{O}(n)$ Non-Adaptive Tester for Unateness

Revisions: 1

Khot and Shinkar (RANDOM, 2016) recently describe an adaptive, $O(n\log(n)/\varepsilon)$-query tester for unateness of Boolean functions $f:\{0,1\}^n \mapsto \{0,1\}$. In this note we describe a simple non-adaptive, $O(n\log(n/\varepsilon)/\varepsilon)$ -query tester for unateness for functions over the hypercube with any ordered range.

more >>>

TR14-042 | 2nd April 2014
Kashyap Dixit, Deeparnab Chakrabarty, Madhav Jha, C. Seshadhri

Property Testing on Product Distributions: Optimal Testers for Bounded Derivative Properties

The primary problem in property testing is to decide whether a given function satisfies a certain property, or is far from any function satisfying it. This crucially requires a notion of distance between functions. The most prevalent notion is the Hamming distance over the {\em uniform} distribution on the domain. ... more >>>

TR13-062 | 18th April 2013
C. Seshadhri, Deeparnab Chakrabarty

An optimal lower bound for monotonicity testing over hypergrids

For positive integers $n, d$, consider the hypergrid $[n]^d$ with the coordinate-wise product partial ordering denoted by $\prec$.
A function $f: [n]^d \mapsto \mathbb{N}$ is monotone if $\forall x \prec y$, $f(x) \leq f(y)$.
A function $f$ is $\varepsilon$-far from monotone if at least an $\varepsilon$-fraction of values must ... more >>>

TR13-029 | 19th February 2013
C. Seshadhri, Deeparnab Chakrabarty

A {\huge ${o(n)}$} monotonicity tester for Boolean functions over the hypercube

Revisions: 1

Given oracle access to a Boolean function $f:\{0,1\}^n \mapsto \{0,1\}$, we design a randomized tester that takes as input a parameter $\eps>0$, and outputs {\sf Yes} if the function is monotone, and outputs {\sf No} with probability $>2/3$, if the function is $\eps$-far from monotone. That is, $f$ needs to ... more >>>

TR12-030 | 4th April 2012
C. Seshadhri, Deeparnab Chakrabarty

Optimal bounds for monotonicity and Lipschitz testing over the hypercube

Revisions: 2

The problem of monotonicity testing of the boolean hypercube is a classic well-studied, yet unsolved
question in property testing. We are given query access to $f:\{0,1\}^n \mapsto R$
(for some ordered range $R$). The boolean hypercube ${\cal B}^n$ has a natural partial order, denoted by $\prec$ (defined by the product ... more >>>

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