# Approximating the Influence of a monotone Boolean function in O(\sqrt{n}) query complexity

@inproceedings{Ron2011ApproximatingTI, title={Approximating the Influence of a monotone Boolean function in O(\sqrt\{n\}) query complexity}, author={Dana Ron and Ronitt Rubinfeld and Shmuel Safra and Omri Weinstein}, booktitle={APPROX-RANDOM}, year={2011} }

The Total Influence (Average Sensitivity) of a discrete function is one of its fundamental measures. We study the problem of approximating the total influe nce of a monotone Boolean function f : f0;1g n ! f 0;1g, which we denote by I[f]. We present a randomized algorithm that approximates the influence of such functions to within a multip licative factor of (1 � �) by performing O � p nlog n I[f] poly(1=�) � queries. We also prove a lower bound of � p n log n·I[f] � on the query complexity of… CONTINUE READING

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