2026-07-20T06:22:53Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6880 2024-03-06T10:39:06Z ddc:004 open_access

The Power and Limitations of Uniform Samples in Testing Properties of Figures Berman, Piotr Murzabulatov, Meiram Raskhodnikova, Sofya Property testing randomized algorithms being a half-plane convexity We investigate testing of properties of 2-dimensional figures that consist of a black object on a white background. Given a parameter epsilon in (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/epsilon) samples. In contrast, we prove that convexity can be tested with O(1/epsilon) queries by testers that can make queries of their choice while uniform testers for this property require Omega(1/epsilon^{5/4}) samples. Previously, the fastest known tester for convexity needed Theta(1/epsilon^{4/3}) queries. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Piotr Berman and Meiram Murzabulatov and Sofya Raskhodnikova 2016 Is Part Of LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2016.45 urn:nbn:de:0030-drops-68803 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.45 eng https://creativecommons.org/licenses/by/3.0/legalcode