# Property Testing with Geometric Queries

@inproceedings{Czumaj2001PropertyTW,
title={Property Testing with Geometric Queries},
author={Artur Czumaj and Christian Sohler},
booktitle={ESA},
year={2001}
}
• Published in ESA 28 August 2001
• Computer Science, Mathematics
This paper investigates geometric problems in the context of property testing algorithms. Property testing is an emerging area in computer science in which one is aiming at verifying whether a given object has a predetermined property or is "far" from any object having the property. Although there has been some research previously done in testing geometric properties, prior works have been mostly dealing with the study of combinatorial notion of the distance defining whether an object is "far…
30 Citations

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• 2007
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### Tolerant Testers of Image Properties

• Computer Science, Mathematics
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• 2016
This work designs efficient approximation algorithms that approximate the distance to three basic properties of image properties within a small additive error ϵ, after reading poly(1/ϵ) pixels, independent of the image size.

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• 2014
The surface area of an unknown n-dimensional set F given membership oracle access is considered, and the algorithm completely evades the "curse of dimensionality": for any n and any κ > 4/π a 1.27, the "approximation factor" of the testing algorithm.

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• Mathematics, Computer Science
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• 2020
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### The Power and Limitations of Uniform Samples in Testing Properties of Figures

• Mathematics
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It is proved that convexity can be tested with $$O({Epsilon }^{-1})$$ queries by testers that can make queries of their choice while uniform testers for this property require $$\varOmega ({\epsilon )^{-5/4}$$ samples.

### Constant-Time Testing and Learning of Image Properties

• Computer Science, Mathematics
ArXiv
• 2015
A systematic study of sublinear-time algorithms for image analysis that have access only to labeled random samples from the input and designs algorithms that approximate the distance to the three properties within a small additive error or, equivalently, tolerant testers for being a half-plane, convexity and connectedness.

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• Computer Science
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• 2006
This work investigates a new class of geometric problems based on the idea of online error correction and provides upper and lower bounds on the complexity of online reconstruction for convexity in 2D and 3D.

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