### Abstract

We present improved algorithms for testing monotonicity of functions. Namely, given the ability to query an unknown function f: Σ^{n} ↦ Ξ where Σ and Ξ are finite ordered sets, 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 _ fraction of the domain). For any ϵ > 0, the query complexity of the test is O((n=/ϵ) · log |Σ| · log

Original language | English (US) |
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Title of host publication | Randomization, Approximation, and Combinatorial Optimization: Algorithms and Techniques - 3rd International Workshop on Randomization and Approximation Techniques in Computer Science and 2nd International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, RANDOM-APPROX 1999, Proceedings |

Publisher | Springer Verlag |

Pages | 97-108 |

Number of pages | 12 |

Volume | 1671 |

ISBN (Print) | 3540663290, 9783540663294 |

DOIs | |

State | Published - 1999 |

Event | 3rd International Workshop on Randomization and Approximation Techniques in Computer Science and 2nd International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, RANDOM-APPROX 1999 - Berkeley, United States Duration: Aug 8 1999 → Aug 11 1999 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1671 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 3rd International Workshop on Randomization and Approximation Techniques in Computer Science and 2nd International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, RANDOM-APPROX 1999 |
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Country | United States |

City | Berkeley |

Period | 8/8/99 → 8/11/99 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Randomization, Approximation, and Combinatorial Optimization: Algorithms and Techniques - 3rd International Workshop on Randomization and Approximation Techniques in Computer Science and 2nd International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, RANDOM-APPROX 1999, Proceedings*(Vol. 1671, pp. 97-108). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1671). Springer Verlag. https://doi.org/10.1007/978-3-540-48413-4_10

**Improved testing algorithms for monotonicity.** / Dodis, Yevgeniy; Goldreich, Oded; Lehman, Eric; Raskhodnikova, Sofya; Ron, Dana; Samorodnitsky, Alex.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Randomization, Approximation, and Combinatorial Optimization: Algorithms and Techniques - 3rd International Workshop on Randomization and Approximation Techniques in Computer Science and 2nd International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, RANDOM-APPROX 1999, Proceedings.*vol. 1671, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1671, Springer Verlag, pp. 97-108, 3rd International Workshop on Randomization and Approximation Techniques in Computer Science and 2nd International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, RANDOM-APPROX 1999, Berkeley, United States, 8/8/99. https://doi.org/10.1007/978-3-540-48413-4_10

}

TY - GEN

T1 - Improved testing algorithms for monotonicity

AU - Dodis, Yevgeniy

AU - Goldreich, Oded

AU - Lehman, Eric

AU - Raskhodnikova, Sofya

AU - Ron, Dana

AU - Samorodnitsky, Alex

PY - 1999

Y1 - 1999

N2 - We present improved algorithms for testing monotonicity of functions. Namely, given the ability to query an unknown function f: Σn ↦ Ξ where Σ and Ξ are finite ordered sets, 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 _ fraction of the domain). For any ϵ > 0, the query complexity of the test is O((n=/ϵ) · log |Σ| · log

AB - We present improved algorithms for testing monotonicity of functions. Namely, given the ability to query an unknown function f: Σn ↦ Ξ where Σ and Ξ are finite ordered sets, 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 _ fraction of the domain). For any ϵ > 0, the query complexity of the test is O((n=/ϵ) · log |Σ| · log

UR - http://www.scopus.com/inward/record.url?scp=84958773905&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958773905&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-48413-4_10

DO - 10.1007/978-3-540-48413-4_10

M3 - Conference contribution

AN - SCOPUS:84958773905

SN - 3540663290

SN - 9783540663294

VL - 1671

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 97

EP - 108

BT - Randomization, Approximation, and Combinatorial Optimization: Algorithms and Techniques - 3rd International Workshop on Randomization and Approximation Techniques in Computer Science and 2nd International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, RANDOM-APPROX 1999, Proceedings

PB - Springer Verlag

ER -