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Related papers: On the computation of edit distance functions

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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.…

Computer Vision and Pattern Recognition · Computer Science 2015-06-01 Brijnesh J. Jain

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,…

Machine Learning · Computer Science 2024-12-30 Qihao Cheng , Da Yan , Tianhao Wu , Zhongyi Huang , Qin Zhang

Sidorenko's conjecture asserts that every bipartite graph $H$ has the property that, for any host graph $G$, the homomorphism density from $H$ to $G$ is asymptotically at least as large as in a quasirandom graph with the same edge density…

Combinatorics · Mathematics 2025-07-22 Yuqi Zhao

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 graph edit distance (GED) measures the dissimilarity between two graphs as the minimal cost of a sequence of elementary operations transforming one graph into another. This measure is fundamental in many areas such as structural pattern…

Data Structures and Algorithms · Computer Science 2019-11-27 Nicolas Boria , David B. Blumenthal , Sébastien Bougleux , Luc Brun

In well-studied graph modification problems, adding and deleting vertices and edges are used as graph editing operations. We propose a model for graph modification on geometric intersection graphs called Geometric Graph Edit Distance that…

Data Structures and Algorithms · Computer Science 2026-04-03 Nicolás Honorato-Droguett , Kazuhiro Kurita , Tesshu Hanaka , Hirotaka Ono

Graph edit distance (GED) is an important similarity measure adopted in a similarity-based analysis between two graphs, and computing GED is a primitive operator in graph database analysis. Partially due to the NP-hardness, the existing…

Databases · Computer Science 2017-10-03 Lijun Chang , Xing Feng , Xuemin Lin , Lu Qin , Wenjie Zhang

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…

Discrete Mathematics · Computer Science 2022-06-14 Arefe Alikhani , Farzad Didehvar

The Discrepancy of a hypergraph is the minimum attainable value, over two-colorings of its vertices, of the maximum absolute imbalance of any hyperedge. The Hereditary Discrepancy of a hypergraph, defined as the maximum discrepancy of a…

Data Structures and Algorithms · Computer Science 2014-07-24 Aleksandar Nikolov , Kunal Talwar

For a family of graphs $\mathcal{F}$, Weighted $\mathcal{F}$-Deletion is the problem for which the input is a vertex weighted graph $G=(V,E)$ and the goal is to delete $S\subseteq V$ with minimum weight such that $G\setminus…

Data Structures and Algorithms · Computer Science 2020-09-03 Jungho Ahn , Eun Jung Kim , Euiwoong Lee

Vertex deletion problems ask whether it is possible to delete at most $k$ vertices from a graph so that the resulting graph belongs to a specified graph class. Over the past years, the parameterized complexity of vertex deletion to a…

Data Structures and Algorithms · Computer Science 2017-08-07 Eduard Eiben , Robert Ganian , O-joung Kwon

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…

Data Structures and Algorithms · Computer Science 2018-11-13 William Kuszmaul

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…

Data Structures and Algorithms · Computer Science 2021-01-01 Shri Prakash Dwivedi

Many applications in pattern recognition represent patterns as a geometric graph. The geometric graph distance (GGD) has recently been studied as a meaningful measure of similarity between two geometric graphs. Since computing the GGD is…

Computational Geometry · Computer Science 2023-06-12 Sushovan Majhi

Let $D$ be a strongly connected digraph. The average distance $\bar{\sigma}(v)$ of a vertex $v$ of $D$ is the arithmetic mean of the distances from $v$ to all other vertices of $D$. The remoteness $\rho(D)$ and proximity $\pi(D)$ of $D$ are…

Combinatorics · Mathematics 2020-01-29 Jiangdong Ai , Stefanie Gerke , Gregory Gutin , Sonwabile Mafunda

Data consisting of a graph with a function mapping into $\mathbb{R}^d$ arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such…

Computational Geometry · Computer Science 2025-07-17 Erin W. Chambers , Elizabeth Munch , Sarah Percival , Bei Wang

Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…

Computational Geometry · Computer Science 2017-12-05 Tamal K. Dey , Dayu Shi , Yusu Wang

Let $G$ be a connected graph. The average distance of a vertex $v$ of $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The proximity and remoteness of $G$ are defined as the minimum and maximum,…

Combinatorics · Mathematics 2025-08-15 Peter Dankelmann , Sonwabile Mafunda , Sufiyan Mallu

Graph similarity search is a common and fundamental operation in graph databases. One of the most popular graph similarity measures is the Graph Edit Distance (GED) mainly because of its broad applicability and high interpretability.…

Databases · Computer Science 2018-01-25 Zijian Li , Xun Jian , Xiang Lian , Lei Chen

Error-tolerant graph matching gathers an important family of problems. These problems aim at finding correspondences between two graphs while integrating an error model. In the Graph Edit Distance (GED) problem, the insertion/deletion of…

Discrete Mathematics · Computer Science 2021-04-19 Romain Raveaux