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arXiv · 2607.27211

Minimal Fillings of Finite Metric Spaces and Convex Polyhedra

A. O. Ivanov·A. A. Tuzhilin
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Abstract

Problem of minimal parametric generalized fillings of finite metric space $M$ (a version of optimal connection problem) leads to construction of a convex multidimensional polyhedra $W_G$ for each tree $G$ connecting $M$ chosen as type of the parametric filling. The weight of the parametric minimal filling can be found as maximum on $W_G$ of the special linear function corresponding to the distance vector of $M$. It is proved that the union of vertex sets of the polyhedra $W_G$ over all possible $G$ forms an extremal subset, i.e., coincides with the vertex set of its convex hull.

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A. O. Ivanov, A. A. Tuzhilin. 2026-05-06. Minimal Fillings of Finite Metric Spaces and Convex Polyhedra. https://arxiv.org/abs/2607.27211

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