Abstract Order Type Extension and New Results on the Rectilinear Crossing Number - Extended Abstract
Oswin Aichholzer, Hannes Krasser · 2005
We provide a complete data base of all realizable order types of 11 points in general position in the plane. Moreover, we develop a novel and efficient method for complete extension to (abstract) order types of size 12 and more. With our approach we have been able to determine the exact rectilinear crossing number for up to n = 17, and slightly improved the asymptotic upper bound. We briefly discuss further applications of this approach.