Abstract order type extension and new results on the rectilinear crossing number

Order Type Extension and New Results ectilinear Crossing Number - Extended Abstract Oswin Aichholzer∗ Hannes Krasser† 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 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.

• Type: Conference
• Year: 2005
• Where: COMPGEOM
• Authors: Oswin Aichholzer, Hannes Krasser
• Keywords: Abstract Oswin Aichholzer∗, COMPGEOM 2005, Discrete Geometry, Order Type Extension, Order Types