@article {IOPORT.01184385,
    author       = {Andrzejak, Artur and Welzl, Emo},
    title        = {Halving point sets.},
    year         = {1998},
    journal      = {Documenta Mathematica},
    issn         = {1431-0643},
    pages        = {471-478},
    publisher    = {Universi\"at Bielefeld, Fakult\"at f\"ur Mathematik, Bielefeld},
    abstract     = {Given $n$ points in $\Bbb R^d$, a hyperplane is called halving if it has at most $\lfloor n/2 \rfloor$ points on either side. This paper surveys known results about the question: How many partitions of a point set (into the points on one side, on the hyperplane, and on the other side) by halving hyperplanes can be realized by an $n$-point set in $R^d$? This is a special case of the famous $k$-set problem. For the planar case the authors discuss the recent upper bound due to {\it T. Dey} [Discrete Comput. Geom. 19, No. 3, 373-382 (1998; Zbl 0899.68107)] and described the Lov\'asz crossing lemma, a useful result in this topic. The remainder of the paper states the known bounds on the number of $j$-facets and presents connections to other topics in discrete geometry and algorithms. These include the upper bound theorem, $k$-levels and parametric matroid optimization.},
    reviewer     = {Jesus De Loera (Minneapolis)},
    identifier   = {01184385},
}