GSF-locality is not sufficient for proximity-oblivious testing

05/18/2021
by   Isolde Adler, et al.
0

In Property Testing, proximity-oblivious testers (POTs) form a class of particularly simple testing algorithms, where a basic test is performed a number of times that may depend on the proximity parameter, but the basic test itself is independent of the proximity parameter. In their seminal work, Goldreich and Ron [STOC 2009; SICOMP 2011] show that the graph properties that allow constant-query proximity-oblivious testing in the bounded-degree model are precisely the properties that can be expressed as a generalised subgraph freeness (GSF) property that satisfies the non-propagation condition. It is left open whether the non-propagation condition is necessary. Indeed, calling properties expressible as a generalised subgraph freeness property GSF-local properties, they ask whether all GSF-local properties are non-propagating. We give a negative answer by exhibiting a property of graphs that is GSF-local and propagating. Hence in particular, our property does not admit a POT, despite being GSF-local. We prove our result by exploiting a recent work of the authors which constructed a first-order (FO) property that is not testable [SODA 2021], and a new connection between FO properties and GSF-local properties via neighbourhood profiles.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

02/15/2021

Testing properties of signed graphs

In graph property testing the task is to distinguish whether a graph sat...
08/13/2020

On Testability of First-Order Properties in Bounded-Degree Graphs

We study property testing of properties that are definable in first-orde...
11/07/2018

Every Testable (Infinite) Property of Bounded-Degree Graphs Contains an Infinite Hyperfinite Subproperty

One of the most fundamental questions in graph property testing is to ch...
07/20/2020

Testing linear inequalities of subgraph statistics

Property testers are fast randomized algorithms whose task is to disting...
05/08/2021

Quantum Proofs of Proximity

We initiate the systematic study of QMA algorithms in the setting of pro...
10/10/2020

A Structural Theorem for Local Algorithms with Applications to Coding, Testing, and Privacy

We prove a general structural theorem for a wide family of local algorit...
11/15/2019

Testing linear-invariant properties

We prove that all linear-invariant, linear-subspace hereditary, locally ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.