Black-Box Complexity: Breaking the O(n logn) Barrier of LeadingOnes

  • Benjamin Doerr
  • Carola Winzen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7401)


We show that the unrestricted black-box complexity of the n-dimensional XOR- and permutation-invariant LeadingOnes function class is O(n log(n) / loglogn). This shows that the recent natural looking O(nlogn) bound is not tight.

The black-box optimization algorithm leading to this bound can be implemented in a way that only 3-ary unbiased variation operators are used. Hence our bound is also valid for the unbiased black-box complexity recently introduced by Lehre and Witt. The bound also remains valid if we impose the additional restriction that the black-box algorithm does not have access to the objective values but only to their relative order (ranking-based black-box complexity).


Algorithms black-box complexity query complexity runtime analysis theory 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Benjamin Doerr
    • 1
  • Carola Winzen
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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