9 citations · 26 across the 10 of their papers we have counts for
4 papers · 1 filter
A generalization of the discrete version of Minkowski's fundamental theorem
Bernardo González Merino, Matthias Henze
One of the most fruitful results from Minkowski's geometric viewpoint on number theory is his so called 1st Fundamental Theorem. It provides an optimal upper bound for the volume o…
Partial-Matching and Hausdorff RMS Distance Under Translation: Combinatorics and Algorithms
Rinat Ben-Avraham, Matthias Henze, Rafel Jaume +4
We consider the RMS distance (sum of squared distances between pairs of points) under translation between two point sets in the plane, in two different setups. In the partial-match…
On extensions of Minkowski's theorem on successive minima
Martin Henk, Matthias Henze, María A. Hernández Cifre
Minkowski's 2nd theorem in the Geometry of Numbers provides optimal upper and lower bounds for the volume of a -symmetric convex body in terms of its successive minima. In this…
Bottleneck Partial-Matching Voronoi Diagrams and Applications
Matthias Henze, Rafel Jaume
Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equally-sized subset of a point set A under translations. We re…