The power and limitations of uniform samples in testing properties of figures

Piotr Berman, Meiram Murzabulatov, Sofya Raskhodnikova

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

We investigate testing of properties of 2-dimensional figures that consist of a black object on a white background. Given a parameter ε ∈ (0, 1/2), a tester for a specified property has to accept with probability at least 2/3 if the input figure satisfies the property and reject with probability at least 2/3 if it does not. In general, property testers can query the color of any point in the input figure. We study the power of testers that get access only to uniform samples from the input figure. We show that for the property of being a half-plane, the uniform testers are as powerful as general testers: they require only O(1/ε) samples. In contrast, we prove that convexity can be tested with O(1/ε) queries by testers that can make queries of their choice while uniform testers for this property require Ω(1/ε5/4) samples. Previously, the fastest known tester for convexity needed Θ(1/ε4/3) queries.

Original languageEnglish (US)
Title of host publication36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2016
EditorsAkash Lal, S. Akshay, Saket Saurabh, Sandeep Sen, Saket Saurabh
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages45.1-45.14
ISBN (Electronic)9783959770279
DOIs
StatePublished - Dec 1 2016
Event36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2016 - Chennai, India
Duration: Dec 13 2016Dec 15 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume65
ISSN (Print)1868-8969

Other

Other36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2016
CountryIndia
CityChennai
Period12/13/1612/15/16

All Science Journal Classification (ASJC) codes

  • Software

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