Approximating the influence of monotone boolean functions in O(√n) query complexity
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Rubinfeld_Approximating the influence.pdf
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Author(s)
Ron, Dana
Rubinfeld, Ronitt
Safra, Muli
Weinstein, Omri
Date Issued
August 2011
Journal
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Publisher
Springer Berlin / Heidelberg
Citation
Ron, Dana et al. “Approximating the influence of monotone boolean functions in O(√n) query complexity.” Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Ed. Leslie Ann Goldberg et al. LNCS Vol. 6845. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. 664–675.
Version
Author's final manuscript
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 f : {0, 1}[superscript n] → {0, 1}, 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([√n log n[over]I[f]] poly(1/Є ))queries. We also prove a lower bound of Ω ([√ n [over] log n·I[f]])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 [over] I[f]]), which matches the complexity of a simple sampling algorithm.
Description
Author Manuscript received 27 Jan 2011. 14th International Workshop, APPROX 2011, and 15th International Workshop, RANDOM 2011, Princeton, NJ, USA, August 17-19, 2011. Proceedings
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/978-3-642-22935-0_56
