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}
}
  • Dana Ron, Ronitt Rubinfeld, +1 author Omri Weinstein
  • Published in APPROX-RANDOM 2011
  • Mathematics, Computer Science
  • 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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