Reducing the Arity in Unbiased Black-Box Complexity
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We show that for all 1<k ≤ n the k-ary unbiased black-box complexity of the n-dimensional function class is O(n/k). This indicates that the power of higher arity operators is much stronger than what the previous O(n/ k) bound by Doerr et al. (Faster black-box algorithms through higher arity operators, Proc. of FOGA 2011, pp. 163--172, ACM, 2011) suggests. The key to this result is an encoding strategy, which might be of independent interest. We show that, using k-ary unbiased variation operators only, we may simulate an unrestricted memory of size O(2^k) bits.
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