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APPROX
2011
Springer

On Approximating the Number of Relevant Variables in a Function

7 years 6 months ago
On Approximating the Number of Relevant Variables in a Function
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. ∗ This work was supported by the Israel Science Foundation (grant number 246/08).
Dana Ron, Gilad Tsur
Added 12 Dec 2011
Updated 12 Dec 2011
Type Journal
Year 2011
Where APPROX
Authors Dana Ron, Gilad Tsur
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