Related papers: Graph Similarity and Approximate Isomorphism
It is unknown whether two graphs can be tested for isomorphism in polynomial time. A classical approach to the Graph Isomorphism Problem is the d-dimensional Weisfeiler-Lehman algorithm. The d-dimensional WL-algorithm can distinguish many…
This work studies fundamental limits for recovering the underlying correspondence among multiple correlated graphs. In the setting of inhomogeneous random graphs, we present and analyze a matching algorithm: first partially match the graphs…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
The mim-width of a graph is a powerful structural parameter that, when bounded by a constant, allows several hard problems to be polynomial-time solvable - with a recent meta-theorem encompassing a large class of problems [SODA2023]. Since…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing…
The spectrum of a network or graph $G=(V,E)$ with adjacency matrix $A$, consists of the eigenvalues of the normalized Laplacian $L= I - D^{-1/2} A D^{-1/2}$. This set of eigenvalues encapsulates many aspects of the structure of the graph,…
Visibility problems have been investigated for a long time under different assumptions as they pose challenging combinatorial problems and are connected to robot navigation problems. The mutual-visibility problem in a graph $G$ of $n$…
For graphs $G$ and $H$, a \emph{homomorphism} from $G$ to $H$ is an edge-preserving mapping from the vertex set of $G$ to the vertex set of $H$. For a fixed graph $H$, by \textsc{Hom($H$)} we denote the computational problem which asks…
Computing efficiently a robust measure of similarity or dissimilarity between graphs is a major challenge in Pattern Recognition. The Graph Edit Distance (GED) is a flexible measure of dissimilarity between graphs which arises in…
Graph matching is one of the most important problems in graph theory and combinatorial optimization, with many applications in various domains. Although meta-heuristic algorithms have had good performance on many NP-Hard and NP-Complete…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graph-structured data. However, as widely used, graph matching that incorporates pairwise…
We propose a novel way of generalizing the class of interval graphs, via a graph width parameter called the simultaneous interval number. This parameter is related to the simultaneous representation problem for interval graphs and defined…
In this paper, we consider the weighted graph matching problem with partially disclosed correspondences between a number of anchor nodes. Our construction exploits recently introduced node signatures based on graph Laplacians, namely the…
Graph matching finds the correspondence of nodes across two correlated graphs and lies at the core of many applications. When graph side information is not available, the node correspondence is estimated on the sole basis of network…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
We consider the problem of sampling from the Ising model when the underlying interaction matrix has eigenvalues lying within an interval of length $\gamma$. Recent work in this setting has shown various algorithmic results that apply…
The notion of forbidden-transition graphs allows for a robust generalization of walks in graphs. In a forbidden-transition graph, every pair of edges incident to a common vertex is permitted or forbidden; a walk is compatible if all pairs…
In the past decades for more and more graph classes the Graph Isomorphism Problem was shown to be solvable in polynomial time. An interesting family of graph classes arises from intersection graphs of geometric objects. In this work we show…