Probabilistic properties of topologies of finite metric spaces' minimal fillings

TL;DR

This paper introduces a probabilistic framework and an algorithm for analyzing minimal fillings of finite additive metric spaces, enabling both theoretical insights and practical computations with confirmed simulation results.

Contribution

It provides a novel method to assign probabilities to minimal fillings and an algorithm for their computation, advancing understanding of their asymptotic properties.

Findings

Probability measures match simulation results

Algorithm efficiently computes minimal fillings

Technique reveals asymptotic ratios for graph families

Abstract

In this work we provide a way to introduce a probability measure on the space of minimal fillings of finite additive metric spaces as well as an algorithm for its computation. The values of probability, got from the analytical solution, coincide with the computer simulation for the computed cases. Also the built technique makes possible to find the asymptotic of the ratio for families of graph structures.