Updating the Number of Crossings of Complete Geometric Graphs.
Frank Duque, Ruy Fabila‐Monroy · arXiv (Cornell University) · 2016
Let $S$ be a set of $n$ points in general poisition in the plane. Let $\overline{cr}(S)$ be number of pairs of edges that cross in a rectilinear drawing of the complete graph with $S$ as its vertex set. Suppose that this number is known. In this paper we consider the problem computing $\overline{cr}(S')$, where $S'$ comes from adding, removing or moving a point from $S$.