Related papers: The edit distance function of some graphs
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…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
Let $G=(V,E)$ be a graph. A $k$-neighborhood in $G$ is a set of vertices consisting of all the vertices at distance at most $k$ from some vertex of $G$. The hypergraph on vertex set $V$ which edge set consists of all the $k$-neighborhoods…
Let $SGL_n(\mathbb{F}_2)$ be the set of all invertible $n\times n$ symmetric matrices over the binary field $\mathbb{F}_2$. Let $\Gamma_n$ be the graph with the vertex set $SGL_n(\mathbb{F}_2)$ where a pair of matrices $\{A,B\}$ form an…
A mixed graph is obtained from a graph by orienting some of its edges. The Hermitian adjacency matrix of a mixed graph with the vertex set $ \{v_{1}, \ldots , v_{n}\} $, is the matrix $ H=[h_{ij}]_{n \times n} $, where $ h_{ij}=-h_{ji}=i $…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
The Steiner distance of a graph, introduced by Chartrand, Oellermann, Tian and Zou in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ and $S\subseteq V(G)$, the…
Finding the graphs that are most similar to a query graph in a large database is a common task with various applications. A widely-used similarity measure is the graph edit distance, which provides an intuitive notion of similarity and…
We present an additive $\varepsilon n^{2}$-approximation algorithm for the Graph Edit Distance problem (GED) on graphs of VC dimension $d$ running in time $n^{O(d/\varepsilon^{2})}$. In particular, this recovers a previous result by Arora,…
Due to their capacity to encode rich structural information, labeled graphs are often used for modeling various kinds of objects such as images, molecules, and chemical compounds. If pattern recognition problems such as clustering and…
Among the most important graph parameters is the Diameter, the largest distance between any two vertices. There are no known very efficient algorithms for computing the Diameter exactly. Thus, much research has been devoted to how fast this…
We say that two graphs $H_1,H_2$ on the same vertex set are $G$-creating ($G$-different in other papers, this difference is explained in the introduction) if the union of the two graphs contains $G$ as a subgraph. Let $H(n,k)$ be the…
A special case of a theorem of De Bruijn and Erd\H{o}s asserts that any noncollinear set of $n$ points in the plane determines at least $n$ distinct lines. Chen and Chv\'atal conjectured a generalization of this result to arbitrary finite…
Linear rank-width is a linearized variation of rank-width, and it is deeply related to matroid path-width. In this paper, we show that the linear rank-width of every $n$-vertex distance-hereditary graph, equivalently a graph of rank-width…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Graph Edit Distance (GED) is a widely used measure of graph similarity, valued for its flexibility in encoding domain knowledge through operation costs. However, existing learning-based approximation methods follow a modeling paradigm that…
Computing the edit distance of two strings is one of the most basic problems in computer science and combinatorial optimization. Tree edit distance is a natural generalization of edit distance in which the task is to compute a measure of…
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…
The edit distance between strings classically assigns unit cost to every character insertion, deletion, and substitution, whereas the Hamming distance only allows substitutions. In many real-life scenarios, insertions and deletions…
We improve the best known upper bound on the number of edges in a unit-distance graph on $n$ vertices for each $n\in\{16,\ldots,30\}$. When $n\leq 21$, our bounds match the best known lower bounds, and we fully enumerate the densest…