On approximating the number of relevant variables in a function

Dana Ron; Gilad Tsur

doi:10.1007/978-3-642-22935-0_57

On approximating the number of relevant variables in a function

Dana Ron^*
, Gilad Tsur

^*Corresponding author for this work

School of Electrical Engineering

Tel Aviv University

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

1 Scopus citations

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.

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings
Pages	676-687
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-22935-0_57
State	Published - 2011
Event	14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011 - Princeton, NJ, United States Duration: 17 Aug 2011 → 19 Aug 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6845 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011
Country/Territory	United States
City	Princeton, NJ
Period	17/08/11 → 19/08/11

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10.1007/978-3-642-22935-0_57

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Ron, D., & Tsur, G. (2011). On approximating the number of relevant variables in a function. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings (pp. 676-687). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6845 LNCS). https://doi.org/10.1007/978-3-642-22935-0_57

Ron, Dana ; Tsur, Gilad. / On approximating the number of relevant variables in a function. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings. 2011. pp. 676-687 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Ron, D & Tsur, G 2011, On approximating the number of relevant variables in a function. in Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6845 LNCS, pp. 676-687, 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011, Princeton, NJ, United States, 17/08/11. https://doi.org/10.1007/978-3-642-22935-0_57

On approximating the number of relevant variables in a function. / Ron, Dana; Tsur, Gilad.
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings. 2011. p. 676-687 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6845 LNCS).

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

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Ron D, Tsur G. On approximating the number of relevant variables in a function. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings. 2011. p. 676-687. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-22935-0_57

On approximating the number of relevant variables in a function

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