On Estimating the Maximum Domination Value and the Skyline Cardinality of Multi-Dimensional Data Sets

The last years there is an increasing interest for query processing techniques that take into consideration the dominance relationship between items to select the most promising ones, based on user preferences. Skyline and top-k dominating queries are examples of such techniques. A skyline query computes the items that are not dominated, whereas a top-k dominating query returns the k items with the highest domination score. To enable query optimization, it is important to estimate the expected number of skyline items as well as the maximum domination value of an item. In this article, we provide an estimation for the maximum domination value under the distinct values and attribute independence assumptions. We provide three different methodologies for estimating and calculating the maximum domination value and we test their performance and accuracy. Among the proposed estimation methods, our method Estimation with Roots outperforms all others and returns the most accurate results. We also introduce the eliminating dimension, i.e. the dimension beyond which all domination values become zero, and we provide an efficient estimation of that dimension. Moreover, we provide an accurate estimation of the skyline cardinality of a data set.