One-dimensional minimal fillings with negative edge weights

2011/01/15 by Z. N. Ovsyannikov, Ivanov, Alexandr O., Natalia P. Strelkova +4 · 1 citation
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1101.3014

openalex publication_date 2011/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Ivanov and Tuzhilin started an investigation of a particular case of Gromov Minimal Fillings problem (generalized to the case of stratified manifolds). Weighted graphs with non-negative weight function were used as minimal fillings of finite metric spaces. In the present paper we introduce generalized minimal fillings, i.e. minimal fillings where the weight function is not necessarily non-negative. We prove that for any finite metric space its minimal filling has the minimum weight in the class of all generalized fillings of the space.

Cited by

• Minimal Fillings of Finite Metric Spaces and Convex Polyhedra

Related

• One-dimensional Gromov minimal filling
• Dual Linear Programming Problem and One-Dimensional Gromov Minimal Fillings of Finite Metric Spaces
• Minimal Fillings of Finite Metric Spaces and Convex Polyhedra
• Probabilistic properties of topologies of finite metric spaces' minimal\n fillings
• Filling volume minimality and boundary rigidity of metrics close to a negatively curved symmetric metric