A Combinatorial Approach to Interleaving Distance between Merge Trees
M. Pegoraro · arXiv (Cornell University) · 2021
In this work we approach the study of the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain an upper bound for such distance. We also tackle the problem of approximating optimal matchings between trees by solving linear integer optimization problems in a recursive and dynamical fashion. This is intended as a first step into a combinatorial understanding of the interleaving distance, which could lead to useful parametrizations of maps between merge trees and to a feasible approach to the exact computation of such distances.