We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES (k) such that any set S of at least fES (k) points in general posit...
Oswin Aichholzer, Thomas Hackl, Clemens Huemer, Fe...
We introduce a general method to count and randomly sample unlabeled combinatorial structures. The approach is based on pointing unlabeled structures in an “unbiased” way, i.e...
A problem of arranging n points as uniformly as possible, which is equivalent to that of packing n equal and non-overlapping circles in a unit square, is frequently asked. In this ...
Given a set P of n points in the plane, the two-circle point-labeling problem consists of placing 2n uniform, non-intersecting, maximum-size open circles such that each point touc...
We consider the problem of determining the placement of a star R on a set P of n points in the plane such that a given objective function is maximized. A star R is a set of m rays...