Tropical Fermat-Weber Polytopes

• DOI: 10.48550/arxiv.2402.14287
• Publication Date: 2024-02-22
• Authors: D. Barnhill; John Sabol; Ruriko Yoshida; Keiji Miura
• Keywords: FOS: Mathematics; Mathematics - Combinatorics; Combinatorics (math.CO)

We study the geometry of tropical Fermat-Weber points in terms symmetric metric over projective torus. It is well known that a point given sample not unique and this paper we show set all possible forms polytrope. Then, introduce gradient using them, polytrope bounded cell hyperplane arrangement by both min- max-tropical hyperplanes with apices which are observations input data.