Andrea de las Heras Parrilla

activity

20212026

collaborators

5 papers

cs.CG2026

A Geometric View of Combinatorial Fiedler Theory

José Fernández Goycoolea, Andrea de las Heras-Parrilla, Luis H. Herrera +2

Recently, Andrade and Dahl introduced combinatorial Fiedler theory by studying a parameter $b (G)$ defined as the $ℓ_{1}$ -analog of the Rayleigh quotient minimization characterizat…

cs.CG2024

Sibson's formula for higher order Voronoi diagrams

Mercè Claverol, Andrea de las Heras-Parrilla, Clemens Huemer +1

Let $S$ be a set of $n$ points in general position in $R^{d}$ . The order- $k$ Voronoi diagram of $S$ , $V_{k} (S)$ , is a subdivision of $R^{d}$ into cells whose points hav…

math.CO2023

On polynomials associated to Voronoi diagrams of point sets and crossing numbers

Mercè Claverol, Andrea de las Heras-Parrilla, David Flores-Peñaloza +2

Three polynomials are defined for given sets $S$ of $n$ points in general position in the plane: The Voronoi polynomial with coefficients the numbers of vertices of the order- $k$ V…

cs.CG2022

Voronoi Diagrams of Arbitrary Order on the Sphere

Mercè Claverol, Andrea de las Heras Parrilla, Clemens Huemer

For a given set of points $U$ on a sphere $S$ , the order $k$ spherical Voronoi diagram $S V_{k} (U)$ decomposes the surface of $S$ into regions whose points have the same $k$ nearest p…

math.CO2021

The edge labeling of higher order Voronoi diagrams

Mercè Claverol, Andrea de las Heras Parrilla, Clemens Huemer +1

We present an edge labeling of order- $k$ Voronoi diagrams, $V_{k} (S)$ , of point sets $S$ in the plane, and study properties of the regions defined by them. Among them, we show that $…