Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids

D Chakrabarty, C Seshadhri - Proceedings of the forty-fifth annual ACM …, 2013 - dl.acm.org
The problem of monotonicity testing over the hypergrid and its special case, the hypercube,
is a classic question in property testing. We are given query access to f:[k] n-> R (for some …

Lp-testing

P Berman, S Raskhodnikova… - Proceedings of the forty …, 2014 - dl.acm.org
We initiate a systematic study of sublinear algorithms for approximately testing properties of
real-valued data with respect to L p distances for p= 1, 2. Such algorithms distinguish …

Lower bounds for testing properties of functions over hypergrid domains

E Blais, S Raskhodnikova… - 2014 IEEE 29th …, 2014 - ieeexplore.ieee.org
We show how the communication complexity method introduced in (Blais, Brody, Matulef
2012) can be used to prove lower bounds on the number of queries required to test …

Property testing on product distributions: Optimal testers for bounded derivative properties

D Chakrabarty, K Dixit, M Jha… - ACM Transactions on …, 2017 - dl.acm.org
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 …

Optimal unateness testers for real-valued functions: Adaptivity helps

R Baleshzar, D Chakrabarty, RKS Pallavoor… - arXiv preprint arXiv …, 2017 - arxiv.org
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 …

Testing hereditary properties of ordered graphs and matrices

N Alon, O Ben-Eliezer, E Fischer - 2017 IEEE 58th Annual …, 2017 - ieeexplore.ieee.org
We consider properties of edge-colored vertex-ordered graphs-graphs with a totally ordered
vertex set and a finite set of possible edge colors-showing that any hereditary property of …

Wasserstein conditional independence testing

A Warren - arXiv preprint arXiv:2107.14184, 2021 - arxiv.org
We introduce a test for the conditional independence of random variables $ X $ and $ Y $
given a random variable $ Z $, specifically by sampling from the joint distribution $(X, Y, Z) …

Online directed spanners and Steiner forests

E Grigorescu, YS Lin, K Quanrud - arXiv preprint arXiv:2103.04543, 2021 - arxiv.org
We present online algorithms for directed spanners and Steiner forests. These problems fall
under the unifying framework of online covering linear programming formulations …

Testing the Lipschitz property over product distributions with applications to data privacy

K Dixit, M Jha, S Raskhodnikova, A Thakurta - Theory of Cryptography …, 2013 - Springer
In the past few years, the focus of research in the area of statistical data privacy has been in
designing algorithms for various problems which satisfy some rigorous notions of privacy …

Erasure-resilient property testing

K Dixit, S Raskhodnikova, A Thakurta, N Varma - SIAM Journal on Computing, 2018 - SIAM
Property testers form an important class of sublinear-time algorithms. In the standard
property testing model, an algorithm accesses the input function f:D↦\calR via an oracle …