Related papers: The edit distance function of some graphs
Edit distance, also known as Levenshtein distance, is an essential way to compare two strings that proved to be particularly useful in the analysis of genetic sequences and natural language processing. However, edit distance is a discrete…
Given a graph pair $(G^1, G^2)$, graph edit distance (GED) is defined as the minimum number of edit operations converting $G^1$ to $G^2$. GED is a fundamental operation widely used in many applications, but its exact computation is NP-hard,…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
The metric dimension, $\dim(G)$, of a graph $G$ is a graph parameter motivated by robot navigation that has been studied extensively. Let $G$ be a graph with vertex set $V(G)$, and let $d(x,y)$ denote the length of a shortest $x-y$ path in…
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…
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…
A graph is distance-hereditary if for any pair of vertices, their distance in every connected induced subgraph containing both vertices is the same as their distance in the original graph. The Distance-Hereditary Vertex Deletion problem…
Distance-hereditary graphs form an important class of graphs, from the theoretical point of view, due to the fact that they are the totally decomposable graphs for the split-decomposition. The previous best enumerative result for these…
A graph is said to be distance-hereditary if the distance function in every connected induced subgraph is the same as in the graph itself. We prove that the ordinary Weisfeiler-Leman algorithm correctly tests the isomorphism of any two…
We show that if the degree sequence of a graph $G$ is close in $\ell_1$-distance to a given realizable degree sequence $(d_1,\dots,d_n)$, then $G$ is close in edit distance to a graph with degree sequence $(d_1,\dots,d_n)$. We then use this…
The edit distance is a fundamental measure of sequence similarity, defined as the minimum number of character insertions, deletions, and substitutions needed to transform one string into the other. Given two strings of length at most $n$,…
The graph edit distance (GED) is a well-established distance measure widely used in many applications. However, existing methods for the GED computation suffer from several drawbacks including oversized search space, huge memory…
In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…
Edit distance is a measure of similarity of two strings based on the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. The edit distance can be computed exactly using a…
We present an algorithm for approximating the edit distance $\operatorname{ed}(x, y)$ between two strings $x$ and $y$ in time parameterized by the degree to which one of the strings $x$ satisfies a natural pseudorandomness property. The…
Graph Edit Distance (GED) is a widely used metric for measuring similarity between two graphs. Computing the optimal GED is NP-hard, leading to the development of various neural and non-neural heuristics. While neural methods have achieved…
The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally (and sometimes proved more easily) in…
Distance measures provide the foundation for many popular algorithms in Machine Learning and Pattern Recognition. Different notions of distance can be used depending on the types of the data the algorithm is working on. For graph-shaped…
The tutorial describes the concept of edit distances applied to research and commercial contexts. We use Translation Edit Rate (TER), Levenshtein, Damerau-Levenshtein, Longest Common Subsequence and $n$-gram distances to demonstrate the…
We introduce the notion of Levenshtein graphs, an analog to Hamming graphs but using the edit distance instead of the Hamming distance; in particular, Levenshtein graphs allow for underlying strings (nodes) of different lengths. We…