Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Total Influence (Average Sensitivity) of a discrete function is one of its fundamental measures.  study the problem of approximating the total influence of a monotone Boolean function f : {0, 1}n → {0, 1}, which  denote by I[f].  present a randomized algorithm that approximates the influence of such functions to within a multiplicative factor of (1 ± e) by performing O(√n log n/I[f] poly(1/e) queries.  also prove a lor bound of Ω(√n/log nċI[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  give a lor bound of Ω(n/I[f]), which matches the complexity of a simple sampling algorithm.
['Dana Ron', 'Ronitt Rubinfeld', 'Muli Safra', 'Omri Weinstein']
I am writing a research paper on a idea Approximating the influence of monotone boolean functions in O(√n) query complexity
[{"from": "human", "value": "I am writing a research paper on a idea Approximating the influence of monotone boolean functions in O(\u221an) query complexity"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Total Influence (Average Sensitivity) of a discrete function is one of its fundamental measures.  study the problem of approximating the total influence of a monotone Boolean function f : {0, 1}n \u2192 {0, 1}, which  denote by I[f].  present a randomized algorithm that approximates the influence of such functions to within a multiplicative factor of (1 \u00b1 e) by performing O(\u221an log n/I[f] poly(1/e) queries.  also prove a lor bound of \u03a9(\u221an/log n\u010bI[f]) on the query complexity of any constant-factor approximation algorithm for this problem (which holds for I[f] = \u03a9(1)), hence showing that our algorithm is almost optimal in terms of its dependence on n. For general functions  give a lor bound of \u03a9(n/I[f]), which matches the complexity of a simple sampling algorithm."}]