TY - GEN
T1 - The power and limitations of uniform samples in testing properties of figures
AU - Berman, Piotr
AU - Murzabulatov, Meiram
AU - Raskhodnikova, Sofya
N1 - Funding Information:
M. M. and S. R. were supported by NSF award CCF-1422975.
Publisher Copyright:
© Piotr Berman, Meiram Murzabulatov, and Sofya Raskhodnikova;.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - 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.
AB - 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.
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U2 - 10.4230/LIPIcs.FSTTCS.2016.45
DO - 10.4230/LIPIcs.FSTTCS.2016.45
M3 - Conference contribution
AN - SCOPUS:85010825621
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 45.1-45.14
BT - 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2016
A2 - Lal, Akash
A2 - Akshay, S.
A2 - Saurabh, Saket
A2 - Sen, Sandeep
A2 - Saurabh, Saket
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2016
Y2 - 13 December 2016 through 15 December 2016
ER -