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 -