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

Dana Ron*, Ronit Rubinfeld, Muli Safra, Alex Samorodnitsky, Omri Weinstein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

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.

Original languageAmerican English
Article number11
JournalACM Transactions on Computation Theory
Volume4
Issue number4
DOIs
StatePublished - Nov 2012

Keywords

  • Influence of a Boolean function
  • Sublinear query approximation algorithms
  • Symmetric chains

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