TY - GEN

T1 - Approximating the influence of monotone boolean functions in O(√n) query complexity

AU - Ron, Dana

AU - Rubinfeld, Ronitt

AU - Safra, Muli

AU - Weinstein, Omri

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80052361585&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-22935-0_56

DO - 10.1007/978-3-642-22935-0_56

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AN - SCOPUS:80052361585

SN - 9783642229343

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 664

EP - 675

BT - Approximation, Randomization, and Combinatorial Optimization

T2 - 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011

Y2 - 17 August 2011 through 19 August 2011

ER -