On the computation of the empirical attainment function

Abstract

Abstract. The attainment function provides a description of the loca-tion of the distribution of a random non-dominated point set. This func-tion can be estimated from experimental data via its empirical counter-part, the empirical attainment function (EAF). However, computation of the EAF in more than two dimensions is a non-trivial task. In this article, the problem of computing the empirical attainment function is formalised, and upper and lower bounds on the corresponding number of output points are presented. In addition, efficient algorithms for the two and three-dimensional cases are proposed, and their time complexities are related to lower bounds derived for each case