@article{4113, abstract = {Let S denote a set of n points in the Euclidean plane. A subset S′ of S is termed a k-set of S if it contains k points and there exists a straight line which has no point of S on it and separates S′ from S−S′. We let fk(n) denote the maximum number of k-sets which can be realized by a set of n points. This paper studies the asymptotic behaviour of fk(n) as this function has applications to a number of problems in computational geometry. A lower and an upper bound on fk(n) is established. Both are nontrivial and improve bounds known before. In particular, is shown by exhibiting special point-sets which realize that many k-sets. In addition, is proved by the study of a combinatorial problem which is of interest in its own right.}, author = {Edelsbrunner, Herbert and Welzl, Emo}, issn = {1096-0899}, journal = {Journal of Combinatorial Theory Series A}, number = {1}, pages = {15 -- 29}, publisher = {Elsevier}, title = {{On the number of line separations of a finite set in the plane}}, doi = {10.1016/0097-3165(85)90017-2}, volume = {38}, year = {1985}, }