TY - GEN

T1 - Testing ±1-weight halfspace

AU - Matulef, Kevin

AU - O'Donnell, Ryan

AU - Rubinfeld, Ronitt

AU - Servedio, Rocco A.

PY - 2009

Y1 - 2009

N2 - We consider the problem of testing whether a Boolean function f : { - 1, 1} n →{- 1, 1} is a ±1-weight halfspace, i.e. a function of the form f(x) = sgn(w 1 x 1 + w 2 x 2 + ⋯ + w n x 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 ∈-far from all such halfspaces we prove that nonadaptive algorithms must make Ω(log n) queries. We complement this lower bound with a sublinear upper bound showing that O(poly queries suffice.

AB - We consider the problem of testing whether a Boolean function f : { - 1, 1} n →{- 1, 1} is a ±1-weight halfspace, i.e. a function of the form f(x) = sgn(w 1 x 1 + w 2 x 2 + ⋯ + w n x 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 ∈-far from all such halfspaces we prove that nonadaptive algorithms must make Ω(log n) queries. We complement this lower bound with a sublinear upper bound showing that O(poly queries suffice.

UR - http://www.scopus.com/inward/record.url?scp=70350589600&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-03685-9_48

DO - 10.1007/978-3-642-03685-9_48

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AN - SCOPUS:70350589600

SN - 3642036848

SN - 9783642036842

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

SP - 646

EP - 657

BT - Approximation, Randomization, and Combinatorial Optimization

T2 - 12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2009 and 13th International Workshop on Randomization and Computation, RANDOM 2009

Y2 - 21 August 2009 through 23 August 2009

ER -