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 …

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 …

Abstract Given P and P'P′, equally sized planar point sets in general position, we call a
bijection from P to P'P′ crossing-preserving if crossings of connecting segments in P are …

We apply ideas from the theory of limits of dense combinatorial structures to study order
types, which are combinatorial encodings of finite point sets. Using flag algebras we obtain …

For many algorithms dealing with sets of points in the plane, the only relevant information
carried by the input is the combinatorial configuration of the points: the orientation of each …

For most algorithms dealing with sets of points in the plane, the only relevant information
carried by the input is the combinatorial configuration of the points: the orientation of each …

This work introduces a novel visual fiducial tag appropriate for applications of automatic
identification. The proposed tag is based in Order Type, a construction defined in …

Let P be a set of n points in the plane, no three in a line. The order type of P specifies, for
every ordered triple, a positive or negative orientation; and the crossing type (for short, x …

The problem to find the matching of two set of points in the plane is solved in this paper,
using a combinatorial invariant from Computational Geometry called Order Type. The …

Abstract Many problems in Combinatorial Geometry ask about the structure of a point set.
Two problems of this kind are the rectilinear crossing number and the number of empty …