TY - JOUR

T1 - Approximating the influence of monotone Boolean functions in O(√n) query complexity

AU - Ron, Dana

AU - Rubinfeld, Ronit

AU - Safra, Muli

AU - Samorodnitsky, Alex

AU - Weinstein, Omri

PY - 2012/11

Y1 - 2012/11

N2 - The Total Influence (Average Sensitivity) of a discrete function is one of its fundamental measures. We study the problem of approximating the total influence of a monotone Boolean function, which we denote by I[f]. We present a randomized algorithm that approximates the influence of such functions to within a multiplicative factor of (1 ± ∈) by performing O (equation) queries. We also prove a lower bound of Ω (equation) on the query complexity of any constant factor approximation algorithm for this problem (which holds for I[f] = Ω(1)), hence showing that our algorithm is almost optimal in terms of its dependence on n. For general functions, we give a lower bound of Ω ([n/I[f]]), which matches the complexity of a simple sampling algorithm.

AB - The Total Influence (Average Sensitivity) of a discrete function is one of its fundamental measures. We study the problem of approximating the total influence of a monotone Boolean function, which we denote by I[f]. We present a randomized algorithm that approximates the influence of such functions to within a multiplicative factor of (1 ± ∈) by performing O (equation) queries. We also prove a lower bound of Ω (equation) on the query complexity of any constant factor approximation algorithm for this problem (which holds for I[f] = Ω(1)), hence showing that our algorithm is almost optimal in terms of its dependence on n. For general functions, we give a lower bound of Ω ([n/I[f]]), which matches the complexity of a simple sampling algorithm.

KW - Influence of a Boolean function

KW - Sublinear query approximation algorithms

KW - Symmetric chains

UR - http://www.scopus.com/inward/record.url?scp=84870691494&partnerID=8YFLogxK

U2 - 10.1145/2382559.2382562

DO - 10.1145/2382559.2382562

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AN - SCOPUS:84870691494

SN - 1942-3454

VL - 4

JO - ACM Transactions on Computation Theory

JF - ACM Transactions on Computation Theory

IS - 4

M1 - 11

ER -