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European Symposium on Algorithms

ESA 2001: Algorithms — ESA 2001 pp 266–277Cite as

Property Testing with Geometric Queries

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2161))

Abstract

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” or it is “close”; very little research has been done for geometric notion of distance measures, that is, distance measures that are based on the geometry underlying input objects.

The main objective of this work is to develop sound models to study geometric problems in the context of property testing. Comparing to the previous work in property testing, there are two novel aspects developed in this paper: geometric measures of being close to an object having the predetermined property, and the use of geometric data structures as basic primitives to design the testers. We believe that the second aspect is of special importance in the context of property testing and that the use of specialized data structures as basic primitives in the testers can be applied to other important problems in this area.

We shall discuss a number of models that in our opinion fit best geometric problems and apply them to study geometric properties for three very fundamental and representative problems in the area: testing convex position, testing map labeling, and testing clusterability.

Research supported in part by an SBR grant No. 421090, by DFG grant Me872/7-1, and by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT).

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Author information

Authors and Affiliations

  1. Department of Computer and Information Science, New Jersey Institute of Technology, University Heights, Newark, NJ, 07102-1982, USA

    Artur Czumaj

  2. Heinz Nixdorf Institute and Department of Mathematics & Computer Science, University of Paderborn, D-33095, Paderborn, Germany

    Christian Sohler

Authors
  1. Artur Czumaj
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  2. Christian Sohler
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science and Heinz Nixdorf Institute, Paderborn University, 33095, Paderborn, Germany

    Friedhelm Meyer auf der Heide

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© 2001 Springer-Verlag Berlin Heidelberg

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Czumaj, A., Sohler, C. (2001). Property Testing with Geometric Queries. In: auf der Heide, F.M. (eds) Algorithms — ESA 2001. ESA 2001. Lecture Notes in Computer Science, vol 2161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44676-1_22

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  • DOI: https://doi.org/10.1007/3-540-44676-1_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42493-2

  • Online ISBN: 978-3-540-44676-7

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