The Power and Limitations of Uniform Samples in Testing Properties of Figures
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.
Property testing
randomized algorithms
being a half-plane
convexity
45:1-45:14
Regular Paper
Piotr
Berman
Piotr Berman
Meiram
Murzabulatov
Meiram Murzabulatov
Sofya
Raskhodnikova
Sofya Raskhodnikova
10.4230/LIPIcs.FSTTCS.2016.45
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