Satisfiability solving has been used to tackle a range of long-standing open math problems
in recent years. We add another success by solving a geometry problem that originated a …

Arrangements of pseudolines are classic objects in discrete and computational geometry.
They have been studied with increasing intensity since their introduction almost 100 years …

Abstract A simple drawing D (G) of a graph G is one where each pair of edges share at most
one point: either a common endpoint or a proper crossing. An edge e in the complement of …

Arrangements of lines and pseudolines are fundamental objects in discrete and
computational geometry. They also appear in other areas of computer science, such as the …

Given a set of points S⊆ R 2, a subset X⊆ S with| X|= k is called k-gon if all points of X lie on
the boundary of the convex hull of X, and k-hole if, in addition, no point of S∖ X lies in the …

Flip graphs of combinatorial and geometric objects are at the heart of many deep structural
insights and connections between different branches of discrete mathematics and computer …

An arrangement of pseudocircles is a collection of simple closed curves on the sphere or in
the plane such that any two of the curves are either disjoint or intersect in exactly two …

Given a separation oracle SO for a convex function f defined on ℝn that has an integral
minimizer inside a box with radius R, we show how to find an exact minimizer of f using at …

We establish the following two main results on order types of points in general position in the
plane (realizable simple planar order types, realizable uniform acyclic oriented matroids of …

Topological drawings are natural representations of graphs in the plane, where vertices are
represented by points, and edges by curves connecting the points. We consider a natural …