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Algorithmic Aspects of Property Testing in the Dense Graphs Model

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2009, RANDOM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5687))

Abstract

In this paper we consider two basic questions regarding the query complexity of testing graph properties in the adjacency matrix model. The first question refers to the relation between adaptive and non-adaptive testers, whereas the second question refers to testability within complexity that is inversely proportional to the proximity parameter, denoted ε. The study of these questions reveals the importance of algorithmic design (also) in this model. The highlights of our study are:

  • A gap between the complexity of adaptive and non-adaptive testers. Specifically, there exists a (natural) graph property that can be tested using \({\widetilde{O}}(\epsilon^{-1})\) adaptive queries, but cannot be tested using o(ε − 3/2) non-adaptive queries.

  • In contrast, there exist natural graph properties that can be tested using \({\widetilde{O}}(\epsilon^{-1})\) non-adaptive queries, whereas Ω(ε − 1) queries are required even in the adaptive case.

We mention that the properties used in the foregoing conflicting results have a similar flavor, although they are of course different.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Weizmann Institute of Science, Rehovot, Israel

    Oded Goldreich

  2. Department of Electrical Engineering-Systems, Tel Aviv University, Tel Aviv, Israel

    Dana Ron

Authors
  1. Oded Goldreich
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  2. Dana Ron
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Editor information

Editors and Affiliations

  1. Dept. of Applied Math and Computer Science, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Irit Dinur

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Technion, Computer Science Department, 32000, Haifa, Israel

    Joseph Naor

  4. University of Geneva, Centre Universitaire d’Informatique, Battelle Bat. A, 7 rte de Drize, 1227, Carouge, Switzerland

    José Rolim

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© 2009 Springer-Verlag Berlin Heidelberg

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Goldreich, O., Ron, D. (2009). Algorithmic Aspects of Property Testing in the Dense Graphs Model. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_39

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  • DOI: https://doi.org/10.1007/978-3-642-03685-9_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03684-2

  • Online ISBN: 978-3-642-03685-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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