  We present a new algorithm for Tukey (halfspace) depth level sets and its
implementation. Given $d$-dimensional data set for any $d\geq 2$, the algorithm
is based on representation of level sets as intersections of balls in $R^d$,
and can be easily adapted to related depths (Type D, Zuo and Serfling (Ann.
Stat. {\bf 28} (2000), 461--482)). The algorithm complexity is $O(dn^2 +
n^2\log{n})$ where $n$ is the data set size. Examples with real and synthetic
data show that the algorithm is much faster than other implemented algorithms
and that it can accept thousands of multidimensional observations, while other
algorithms are tested with two-dimensional data or with a couple of hundreds
multidimensional observations.
