Improved testing algorithms for monotonicity

Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, Alex Samorodnitsky

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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

Original languageEnglish (US)
Title of host publicationRandomization, 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
PublisherSpringer Verlag
Pages97-108
Number of pages12
Volume1671
ISBN (Print)3540663290, 9783540663294
DOIs
StatePublished - 1999
Event3rd 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 1999Aug 11 1999

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1671
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other3rd International Workshop on Randomization and Approximation Techniques in Computer Science and 2nd International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, RANDOM-APPROX 1999
CountryUnited States
CityBerkeley
Period8/8/998/11/99

Fingerprint

Monotonicity
Monotone
Query Complexity
Testing
Monotone Function
Ordered Set
Finite Set
Query
Unknown

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Dodis, Y., Goldreich, O., Lehman, E., Raskhodnikova, S., Ron, D., & Samorodnitsky, A. (1999). Improved testing algorithms for monotonicity. In 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.

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 Springer Verlag, 1999. p. 97-108 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1671).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Dodis, Y, Goldreich, O, Lehman, E, Raskhodnikova, S, Ron, D & Samorodnitsky, A 1999, Improved testing algorithms for monotonicity. in 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
Dodis Y, Goldreich O, Lehman E, Raskhodnikova S, Ron D, Samorodnitsky A. Improved testing algorithms for monotonicity. In 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. Springer Verlag. 1999. p. 97-108. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-540-48413-4_10
Dodis, Yevgeniy ; Goldreich, Oded ; Lehman, Eric ; Raskhodnikova, Sofya ; Ron, Dana ; Samorodnitsky, Alex. / Improved testing algorithms for monotonicity. 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 Springer Verlag, 1999. pp. 97-108 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{3799482605ff494eb4fcfca84be9aa4b,
title = "Improved testing algorithms for monotonicity",
abstract = "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",
author = "Yevgeniy Dodis and Oded Goldreich and Eric Lehman and Sofya Raskhodnikova and Dana Ron and Alex Samorodnitsky",
year = "1999",
doi = "10.1007/978-3-540-48413-4_10",
language = "English (US)",
isbn = "3540663290",
volume = "1671",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "97--108",
booktitle = "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",

}

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 -