Here we store the experimental results described in

- M. Balko and J. Kynčl.
*Bounding the pseudolinear crossing number of K*_{n} via simulated annealing, Extended abstract in the (informal) *Proceedings of the XVI Spanish Meeting on Computational Geometry*, pages 37-40, 2015. [booklet of abstracts]

**Abstract:**
A drawing *D* of a graph is pseudolinear if the edges of *D* can be extended to doubly-infinite curves that form an arrangement of pseudolines. The pseudolinear crossing number of *K*_{n}, denoted by cr(*K*_{n}), is the minimum number of crossings in a pseudolinear drawing of *K*_{n}. Using simulated annealing, we obtain new pseudolinear drawings of *K*_{n} with few crossings for small values of *n*. We introduce a pseudolinear version of known constructions that blow up rectilinear drawings of *K*_{n} and we improve an upper bound for the leading constant in cr(*K*_{n}) to 0.380448, shrinking the current gap between the lower and upper
bound by roughly five percent.

Further details can be found in the paper.

**Results:**
Every pseudolinear drawing of *K*_{n} can be decribed by specifying the orientation of each of its triangles. The *n*-signature of a drawing is the vector of these orientations.
Every pseudolinear drawing of *K*_{n} is thus stored as a {+,-}-vector whose length is the number of triples of vertices of *K*_{n}.
The coordinates of this vector are triples (*a*,*b*,*c*), 1 <= *a* < *b* < *c* <= *n*, in the lexicographic order where a triple is assigned + if the corresponding triangle in *D* is oriented counterclockwise and - otherwise.
For *n* even, we also store a halving matching contained in the corresponding drawing of *K*_{n}.
We recall that *f* : [*n*] → [*n*] is a halving matching in a pseudolinear drawing *D* of *K*_{n} if for every element *i* from [*n*] the pair {*i*, *f*(*i*)} is a halving pair in *D* and there are no distinct *i*, *j* in [*n*] with *f*(*i*) = *j* and *f*(*j*) = *i*.
A halving matching *f* is represented with pairs *i*:*f(i)* for every *i* from [*n*].

A compressed directory with all drawings: [ZIP, 121 kB]

Last update: 28.11.2016