Almost Tight Upper Bound for Finding Fourier Coefficients of Bounded Pseudo- Boolean Functions

A pseudo-Boolean function is a real-valued function defined on {0, 1}n . A k-bounded function is a pseudo-Boolean function that can be expressed as a sum of subfunctions each of which depends on at most k input bits. The k-bounded functions for constant k play an important role in a number of research areas including molecular biology, biophysics, and evolutionary computation. In this paper, we consider the problem of finding the Fourier coefficients of k-bounded functions with a series of function evaluations at any input strings. Suppose that a k-bounded function f with m non-zero Fourier coefficients is given. Our main result is to present an adaptive randomized algorithm to find the Fourier coefficients of f with high probability in O (m log n) function evaluations for constant k. Up to date, the best known upper bound is O ((n, m)m log n), where (n, m) is between n 1 2 and n depending on m. Thus, our bound improves the previous bound by a factor of n 1 2 . Also, it is almost tig...

• Type: Conference
• Year: 2008
• Where: COLT
• Authors: Sung-Soon Choi, Kyomin Jung, Jeong Han Kim
• Keywords: COLT 2008, Fourier Coefficients, K-bounded Function, Machine Learning, Pseudo-Boolean Function