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On Approximating the Number of Relevant Variables in a Function

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2011, RANDOM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6845))

Abstract

In this work we consider the problem of approximating the number of relevant variables in a function given query access to the function. Since obtaining a multiplicative factor approximation is hard in general, we consider several relaxations of the problem. In particular, we consider a relaxation of the property testing variant of the problem and we consider relaxations in which we have a promise that the function belongs to a certain family of functions (e.g., linear functions). In the former relaxation the task is to distinguish between the case that the number of relevant variables is at most k, and the case in which it is far from any function in which the number of relevant variable is more than (1 + γ)k for a parameter γ. We give both upper bounds and almost matching lower bounds for the relaxations we study.

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Authors
  1. Dana Ron
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  2. Gilad Tsur
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Liverpool, Ashton Building, L69 3BX, Liverpool, UK

    Leslie Ann Goldberg

  2. Department of Computer Science, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, 15213, Pittsburgh, PA, USA

    R. Ravi

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

    José D. P. Rolim

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© 2011 Springer-Verlag Berlin Heidelberg

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Ron, D., Tsur, G. (2011). On Approximating the Number of Relevant Variables in a Function. In: Goldberg, L.A., Jansen, K., Ravi, R., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2011 2011. Lecture Notes in Computer Science, vol 6845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22935-0_57

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  • DOI: https://doi.org/10.1007/978-3-642-22935-0_57

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22934-3

  • Online ISBN: 978-3-642-22935-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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