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Testing Monotonicity

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Combinatorica Aims and scope Submit manuscript

at arguments of its choice, the test always accepts a monotone f, and rejects f with high probability if it is ε-far from being monotone (i.e., every monotone function differs from f on more than an ε fraction of the domain). The complexity of the test is O(n/ε).

The analysis of our algorithm relates two natural combinatorial quantities that can be measured with respect to a Boolean function; one being global to the function and the other being local to it. A key ingredient is the use of a switching (or sorting) operator on functions.

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Authors and Affiliations

  1. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science; Rehovot, Israel; E-mail: oded@wisdom.weizmann.ac.il, , , , , , IL

    Oded Goldreich

  2. Laboratory for Computer Science, MIT; 545 Technology Sq., Cambridge, MA 02139, USA; E-mail: shafi@theory.lcs.mit.edu, , , , , , US

    Shafi Goldwasser

  3. Laboratory for Computer Science, MIT; 545 Technology Sq., Cambridge, MA 02139, USA; E-mail: e_lehman@theory.lcs.mit.edu, , , , , , US

    Eric Lehman

  4. Department of EE – Systems, Tel Aviv University; Ramat Aviv, Israel; E-mail: danar@eng.tau.ac.il, , , , , , IL

    Dana Ron

  5. School of Mathematics, Institute for Advanced Study; Olden Lane, Princeton, NJ 08540, USA; E-mail: asamor@ias.edu, , , , , , US

    Alex Samorodnitsky

Authors
  1. Oded Goldreich
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  2. Shafi Goldwasser
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  3. Eric Lehman
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  4. Dana Ron
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  5. Alex Samorodnitsky
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Received March 29, 1999

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Goldreich, O., Goldwasser, S., Lehman, E. et al. Testing Monotonicity. Combinatorica 20, 301–337 (2000). https://doi.org/10.1007/s004930070011

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  • DOI: https://doi.org/10.1007/s004930070011

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