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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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}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,±ε) by performing O(√n log n/I[f] poly(1/ε)) queries. We also prove a lower bound of Ω(√n/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/I[f]), which matches the complexity of a simple sampling algorithm.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings
Pages664-675
Number of pages12
DOIs
StatePublished - 2011
Event14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011 - Princeton, NJ, United States
Duration: 17 Aug 201119 Aug 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6845 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011
Country/TerritoryUnited States
CityPrinceton, NJ
Period17/08/1119/08/11

Fingerprint

Dive into the research topics of 'Approximating the influence of monotone boolean functions in O(√n) query complexity'. Together they form a unique fingerprint.

Cite this