Voronoi diagrams of algebraic varieties under polyhedral norms

We study Voronoi diagrams of manifolds and varieties with respect to polyhedral norms. We provide upper and lower bounds on the dimensions of Voronoi cells. For algebraic varieties, we count their full-dimensional Voronoi cells. As an application, we consider the polyhedral Wasserstein distance between discrete probability distributions. & COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

We study Voronoi diagrams with respect to polyhedral norms for manifolds and varieties. Upper and lower bounds on the dimensions of Voronoi cells are provided. We also examine the full-dimensional Voronoi cells for algebraic varieties. As an application, the polyhedral Wasserstein distance between discrete probability distributions is considered.