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Skylines emerged as a useful notion in database queries for selectingrepresentative groups in multivariate data samples for further decision making,multi-objective optimization or data processing, and the $k$-dominant skylineswere naturally introduced to resolve the abundance of skylines when thedimensionality grows or when the coordinates are negatively correlated. Weprove in this paper that the expected number of $k$-dominant skylines isasymptotically zero for large samples when $1\le k\le d-1$ under two reasonable(continuous) probability assumptions of the input points, $d$ being the(finite) dimensionality, in contrast to the asymptotic unboundedness when$k=d$. In addition to such an asymptotic zero-infinity property, we alsoestablish a sharp threshold phenomenon for the expected ($d-1$)-dominantskylines when the dimensionality is allowed to grow with $n$. Several relatedissues such as the dominant cycle structures and numerical aspects, are alsobriefly studied.

Threshold phenomena in k-dominant skylines of random samples