— This paper presents a method for a planar rigid body consisting of multiple convex bodies to explore an unknown planar workspace, i.e., an unknown configuration space diffeomo...
Given an edge-weighted graph where all weights are nonnegative reals, an edge reweighting is an assignment of nonnegative reals to edges such that, for each vertex, the sums of giv...
We show that recognizing intersection graphs of convex sets has the same complexity as deciding truth in the existential theory of the reals. Comparing this to similar results on t...
Geometric constructions applied to a rational action of an algebraic group lead to a new algorithm for computing rational invariants. A finite generating set of invariants appear...
Abstract. We study the grid size that is needed to represent intersection graphs of convex polygons. Here the polygons are similar to a base polygon P whose corners have rational c...