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… 

Testing Geometric Properties ∗ †

TLDR
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

  • D. Ron
  • Computer Science, Mathematics
    Found. Trends Theor. Comput. Sci.
  • 2009
TLDR
This monograph surveys results in property testing, where the emphasis is on common analysis and algorithmic techniques.

Abstract combinatorial programs and efficient property testers

  • A. CzumajC. Sohler
  • Computer Science, Mathematics
    The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
  • 2002
TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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.

References

SHOWING 1-10 OF 28 REFERENCES

Combinatorial property testing (a survey)

  • Oded Goldreich
  • Mathematics
    Randomization Methods in Algorithm Design
  • 1997
TLDR
This work considers the question of determining whether a given object has a predetermined property or is \far" from any object having the property, and focuses on combinatorial properties, and speciically on graph properties.

Property testing and its connection to learning and approximation

TLDR
The authors study the question of determining whether an unknown function has a particular property or is /spl epsiv/-far from any function with that property, and devise algorithms to test whether a graph has properties such as being k-colorable or having a /spl rho/-clique.

Efficient Testing of Large Graphs

TLDR
This theorem is used to prove that first order graph properties not containing a quantifier alternation of type "/spl forall//spl exist/" are always testable, while it is shown that some properties containing this alternation are not.

Property Testing in Computational Geometry

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

A Sublinear Bipartiteness Tester for Bounded Degree Graphs

TLDR
The contrapositive statement by which slow convergence implies small cuts in the graph is applied, and this implication is applied in showing that for any graph, the graph vertices can be divided into disjoint subsets such that each subset itself exhibits a certain mixing property that is useful in the analysis.

Testing of function that have small width branching programs

  • I. Newman
  • Computer Science
    Proceedings 41st Annual Symposium on Foundations of Computer Science
  • 2000
TLDR
This work generalizes the results of (Alon et al., 1999) asserting that regular languages are efficiently (/spl epsiv/,O(1))-testable.

A packing problem with applications to lettering of maps

The following packing problem arises in connection with lettering of maps: Given n distinct points pl, p2, . . . . pn in the plane, determine the supremum uoPi of all reals U, such that there are n

Map labeling and its generalizations

TLDR
A bicriteria version of the map-labeling problem is formulated and polynomial-time approximation schemes for a number of such problems are provided.

Testing of clustering

TLDR
This work studies the problem of clustering with respect to the diameter and the radius costs from within the framework of property testing and distinguishes between the case when X is (k,b)-clusterable and the case ...

NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs

TLDR
The approximation schemes for hierarchically specified unit disk graphs presented in this paper are among the first approximation schemes in the literature for natural PSPACE-hard optimization problems.