The Reeb Graph Edit Distance is Universal
Ulrich Bauer, Claudia Landi, Facundo Mémoli
Abstract
Abstract We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it provides an upper bound to any other stable distance. In contrast, via a specific construction, we show that the interleaving distance and the functional distortion distance on Reeb graphs are not universal.
Topics & Concepts
MathematicsInfimum and supremumPiecewise linear functionCombinatoricsUpper and lower boundsGraphDiscrete mathematicsPiecewiseNorm (philosophy)Bounded functionGraph theoryDistortion (music)Topological and Geometric Data AnalysisAdvanced Graph Neural NetworksGraph Theory and Algorithms