Testing +/- 1-Weight Halfspaces
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Author(s)
Matulef, Kevin M.
O'Donnell, Ryan
Rubinfeld, Ronitt
Sevedio, Rocco A.
Date Issued
2009
Journal
Lecture Notes in Computer Science
Publisher
Springer Berlin Heidelberg
Citation
Matulef, Kevin et al. “Testing ±1-weight halfspace.” Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques 2009.
Version
Author's final manuscript
Abstract
We consider the problem of testing whether a Boolean function f:{ − 1,1} [superscript n] →{ − 1,1} is a ±1-weight halfspace, i.e. a function of the form f(x) = sgn(w [subscript 1] x [subscript 1] + w [subscript 2] x [subscript 2 ]+ ⋯ + w [subscript n] x [subscript n] ) where the weights w i take values in { − 1,1}. We show that the complexity of this problem is markedly different from the problem of testing whether f is a general halfspace with arbitrary weights. While the latter can be done with a number of queries that is independent of n [7], to distinguish whether f is a ±-weight halfspace versus ε-far from all such halfspaces we prove that nonadaptive algorithms must make Ω(logn) queries. We complement this lower bound with a sublinear upper bound showing that $O(\sqrt{n}\cdot $poly$(\frac{1}{\epsilon}))$ queries suffice.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Attribution-Noncommercial-Share Alike 3.0 Unported
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DOI of Published Version
http://dx.doi.org/10.1007/978-3-642-03685-9_48
