# Property Testing with Geometric Queries

@inproceedings{Czumaj2001PropertyTW, title={Property Testing with Geometric Queries}, author={Artur Czumaj and Christian Sohler}, booktitle={ESA}, year={2001} }

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

### Testing Geometric Properties ∗ †

- Mathematics, Computer Science
- 2007

It is shown that many basic geometric properties have very efficient testing algorithms, whose running time is significantly smaller than the object description size.

### Algorithmic and Analysis Techniques in Property Testing

- Computer Science, MathematicsFound. Trends Theor. Comput. Sci.
- 2009

This monograph surveys results in property testing, where the emphasis is on common analysis and algorithmic techniques.

### Abstract combinatorial programs and efficient property testers

- Computer Science, MathematicsThe 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
- 2002

A novel framework for analyzing property testing algorithms with one-sided error is presented and it is shown that if the problem of testing a property can be reduced to an abstract combinatorial program of small dimension, then the property has an efficient tester.

### Property testing: theory and applications

- Mathematics, Computer Science
- 2003

This thesis investigates properties that are and are not testable with sublinear query complexity of property testing as applied to images and shows that testing properties defined by 2CNF formulas is equivalent, with respect to the number of required queries, to several other function and graph testing problems.

### Tolerant Testers of Image Properties

- Computer Science, MathematicsICALP
- 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.

### Testing Surface Area

- Computer Science, MathematicsSODA
- 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.

### Property Testing of LP-Type Problems

- Mathematics, Computer ScienceICALP
- 2020

This work supplies a tight upper bound on the query complexity of testing clusterability with one cluster considered by Alon, Dar, Parnas, and Ron (FOCS 2000) and supply a corresponding tight lower bound for this problem and other LP-Type problems using geometric constructions.

### The Power and Limitations of Uniform Samples in Testing Properties of Figures

- MathematicsAlgorithmica
- 2018

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, MathematicsArXiv
- 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.

### Online geometric reconstruction

- Computer ScienceSCG '06
- 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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