Related papers: Computing Approximate Graph Edit Distance via Opti…
The graph edit distance (GED) is a flexible distance measure which is widely used for inexact graph matching. Since its exact computation is NP-hard, heuristics are used in practice. A popular approach is to obtain upper bounds for GED via…
The graph traversal edit distance (GTED), introduced by Ebrahimpour Boroojeny et al.~(2018), is an elegant distance measure defined as the minimum edit distance between strings reconstructed from Eulerian trails in two edge-labeled graphs.…
Transportation cost is an attractive similarity measure between probability distributions due to its many useful theoretical properties. However, solving optimal transport exactly can be prohibitively expensive. Therefore, there has been…
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…
Current Graph Neural Networks (GNN) architectures generally rely on two important components: node features embedding through message passing, and aggregation with a specialized form of pooling. The structural (or topological) information…
The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…
Removing overlaps is a central task in domains such as scheduling, visibility, and map labelling. This can be modelled using graphs, where overlap removals correspond to enforcing a certain sparsity constraint on the graph structure. We…
An edge-operation on a graph $G$ is defined to be either the deletion of an existing edge or the addition of a nonexisting edge. Given a family of graphs $\mathcal{G}$, the editing distance from $G$ to $\mathcal{G}$ is the smallest number…
Recently, more and more research has focused on using Graph Neural Networks (GNN) to solve the Graph Similarity Computation problem (GSC), i.e., computing the Graph Edit Distance (GED) between two graphs. These methods treat GSC as an…
We propose a novel graph visualization method leveraging random walk-based embeddings to replace costly graph-theoretical distance computations. Using word2vec-inspired embeddings, our approach captures both structural and semantic…
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…
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
Node similarity is a fundamental problem in graph analytics. However, node similarity between nodes in different graphs (inter-graph nodes) has not received a lot of attention yet. The inter-graph node similarity is important in learning a…
In this paper, we study the problem of graph similarity search with graph edit distance (GED) constraints. Due to the NP-hardness of GED computation, existing solutions to this problem adopt the filtering-and-verification framework with a…
Feature-based image matching has extensive applications in computer vision. Keypoints detected in images can be naturally represented as graph structures, and Graph Neural Networks (GNNs) have been shown to outperform traditional deep…
We present GeGnn, a learning-based method for computing the approximate geodesic distance between two arbitrary points on discrete polyhedra surfaces with constant time complexity after fast precomputation. Previous relevant methods either…
We introduce an optimal transport based approach for comparing undirected graphs with non-negative edge weights and general vertex labels, and we study connections between the resulting linear program and the graph isomorphism problem. Our…
The ability to compute similarity scores between graphs based on metrics such as Graph Edit Distance (GED) is important in many real-world applications. Computing exact GED values is typically an NP-hard problem and traditional algorithms…
We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs,…
The graph matching problem seeks to find an alignment between the nodes of two graphs that minimizes the number of adjacency disagreements. Solving the graph matching is increasingly important due to it's applications in operations…