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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > MONOTONICITY:
Reports tagged with Monotonicity:
TR99-017 | 4th June 1999
Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, Alex Samorodnitsky

Improved Testing Algorithms for Monotonicity.

Revisions: 1


We present improved algorithms for testing monotonicity of functions.
Namely, given the ability to query an unknown function $f$, where
$\Sigma$ and $\Xi$ are finite ordered sets, the test always accepts a
monotone $f$, and rejects $f$ with high probability if it is $\e$-far
from being monotone (i.e., every ... more >>>


TR01-008 | 6th November 2000
Eldar Fischer

On the strength of comparisons in property testing

An $\epsilon$-test for a property $P$ of functions from
${\cal D}=\{1,\ldots,d\}$ to the positive integers is a randomized
algorithm, which makes queries on the value of an input function at
specified locations, and distinguishes with high probability between the
case of the function satisfying $P$, and the case that it ... more >>>


TR04-010 | 26th January 2004
Michal Parnas, Dana Ron, Ronitt Rubinfeld

Tolerant Property Testing and Distance Approximation


A standard property testing algorithm is required to determine
with high probability whether a given object has property
P or whether it is \epsilon-far from having P, for any given
distance parameter \epsilon. An object is said to be \epsilon-far
from having ... more >>>


TR10-048 | 24th March 2010
David GarcĂ­a Soriano, Arie Matsliah, Sourav Chakraborty, Jop Briet

Monotonicity Testing and Shortest-Path Routing on the Cube

We study the problem of monotonicity testing over the hypercube. As
previously observed in several works, a positive answer to a natural question about routing
properties of the hypercube network would imply the existence of efficient
monotonicity testers. In particular, if any $\ell$ disjoint source-sink pairs
on the directed hypercube ... more >>>


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

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 >>>


TR12-075 | 12th June 2012
Pranjal Awasthi, Madhav Jha, Marco Molinaro, Sofya Raskhodnikova

Limitations of Local Filters of Lipschitz and Monotone Functions

We study local filters for two properties of functions $f:\B^d\to \mathbb{R}$: the Lipschitz property and monotonicity. A local filter with additive error $a$ is a randomized algorithm that is given black-box access to a function $f$ and a query point $x$ in the domain of $f$. Its output is a ... more >>>


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

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 >>>


TR13-036 | 13th March 2013
Eric Blais, Sofya Raskhodnikova, Grigory Yaroslavtsev

Lower Bounds for Testing Properties of Functions on Hypergrid Domains

Revisions: 1

We introduce strong, and in many cases optimal, lower bounds for the number of queries required to nonadaptively test three fundamental properties of functions $ f : [n]^d \rightarrow \mathbb R$ on the hypergrid: monotonicity, convexity, and the Lipschitz property.
Our lower bounds also apply to the more restricted setting ... more >>>


TR13-187 | 27th December 2013
Peyman Afshani, Kevin Matulef, Bryan Wilkinson

Property Testing on Linked Lists

Revisions: 1

We define a new property testing model for algorithms that do not have arbitrary query access to the input, but must instead traverse it in a manner that respects the underlying data structure in which it is stored. In particular, we consider the case when the underlying data structure is ... more >>>


TR14-144 | 30th October 2014
Eric Blais, Clement Canonne, Igor Carboni Oliveira, Rocco Servedio, Li-Yang Tan

Learning circuits with few negations

Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and ... more >>>


TR16-136 | 31st August 2016
Clement Canonne, Elena Grigorescu, Siyao Guo, Akash Kumar, Karl Wimmer

Testing k-Monotonicity

Revisions: 1

A Boolean $k$-monotone function defined over a finite poset domain ${\cal D}$ alternates between the values $0$ and $1$ at most $k$ times on any ascending chain in ${\cal D}$. Therefore, $k$-monotone functions are natural generalizations of the classical monotone functions, which are the $1$-monotone functions.

Motivated by the ... more >>>


TR17-103 | 12th June 2017
Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, Nithin Varma

Parameterized Property Testing of Functions

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 >>>




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