We improve the best known upper bound for the bracketing number of d-dimensional axis-parallel boxes anchored in 0 (or, put differently, of lower left orthants intersected with the d-dimensional unit cube [0,1]d). More precisely, we provide a better estimate for the cardinality of an algorithmic bracketing cover construction due to Eric Thiémard, which forms the core of his algorithm to approximate the star discrepancy of arbitrary point sets from [E. Thiémard, An algorithm to compute bounds for the star discrepancy, J. Complexity 17 (2001), 850 – 880]. Moreover, the new upper bound for the bracketing number of anchored axis-parallel boxes yields an improved upper estimate for the bracketing number of arbitrary axis-parallel boxes in [0,1]d. In our upper bounds all constants are fully explicit.

Motivated by neutrality observed in natural evolution often redundant encodings are used in evolutionary algorithms. Many experimental studies have been carried out on this topic. In this paper we present a first rigorous runtime analysis on the effect of using neutrality. We consider a simple model where a layer of constant fitness is distributed in the search space and point out situations where the use of neutrality significantly influence the runtime of an evolutionary algorithm.