Related papers: A Finitely Stable Edit Distance for Merge Trees

The emergence of geometric deep learning as a novel framework to deal with graph-based representations has faded away traditional approaches in favor of completely new methodologies. In this paper, we propose a new framework able to combine…

Edit distance is a fundamental measure of distance between strings and has been widely studied in computer science. While the problem of estimating edit distance has been studied extensively, the equally important question of actually…

In graph theory, a tree is one of the more popular families of graphs with a wide range of applications in computer science as well as many other related fields. While there are several distance measures over the set of all trees, we…

This report evaluates the efficiency of Graph Edit Distance (GED) computation for graph similarity search, comparing Cascading Metric Trees (CMT) with brute-force verification. Despite the anticipated advantages of CMT, our findings…

Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…

The purpose of this paper is to extend the definition of Frechet distance which measures the distance between two curves to a distance (Frechet-Like distance) which measures the similarity between two rooted trees. The definition of…

Wasserstein distance, which measures the discrepancy between distributions, shows efficacy in various types of natural language processing (NLP) and computer vision (CV) applications. One of the challenges in estimating Wasserstein distance…

We introduce a refinement of the persistence diagram, the graded persistence diagram. It is the Mobius inversion of the graded rank function, which is obtained from the rank function using the unary numeral system. Both persistence diagrams…

For a vertex $v$ of a graph $G$, a spanning tree $T$ of $G$ is distance-preserving from $v$ if, for any vertex $w$, the distance from $v$ to $w$ on $T$ is the same as the distance from $v$ to $w$ on $G$. If two vertices $u$ and $v$ are…

We build a functorial pipeline for persistent homology. The input to this pipeline is a filtered simplicial complex indexed by any finite metric lattice and the output is a persistence diagram defined as the M\"obius inversion of its…

CONTEXT. Attack treesare a recommended threat modeling tool, but there is no established method to compare them. OBJECTIVE. We aim to establish a method to compare "real" attack trees, based on both the structure of the tree itself and the…

We establish maximal trees and graphs for the difference of average distance and proximity proving thus the corresponding conjecture posed in [4]. We also establish maximal trees for the difference of average eccentricity and remoteness and…

We prove that the normalized edit distance proposed in [Marzal and Vidal 1993] is a metric when the cost of all the edit operations are the same. This closes a long standing gap in the literature where several authors noted that this…

The concept of $n$-distance was recently introduced to generalize the classical definition of distance to functions of $n$ arguments. In this paper we investigate this concept through a number of examples based on certain geometrical…

Recently, a Wasserstein-type distance for Gaussian mixture models has been proposed. However, that framework can only be generalized to identifiable mixtures of general elliptically contoured distributions whose components come from the…

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…

Given two strings of length $n$ over alphabet $\Sigma$, and an upper bound $k$ on their edit distance, the algorithm of Myers (Algorithmica'86) and Landau and Vishkin (JCSS'88) computes the unweighted string edit distance in…

Agreement forests continue to play a central role in the comparison of phylogenetic trees since their introduction more than 25 years ago. More specifically, they are used to characterise several distances that are based on tree…

We establish tight bi-Lipschitz bounds certifying quasi-universality (universality up to a constant factor) for various distances between Reeb graphs: the interleaving distance, the functional distortion distance, and the functional…

We contribute to the discussion on parsing performance in NLP by introducing a measurement that evaluates the differences between the distributions of edge displacement (the directed distance of edges) seen in training and test data. We…