Related papers: Matching through Embedding in Dense Graphs
In the Exact Matching problem, we are given a graph whose edges are colored red or blue and the task is to decide for a given integer k, if there is a perfect matching with exactly k red edges. Since 1987 it is known that the Exact Matching…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these…
The Metric Embedding problem takes as input two metric spaces $(X,D_X)$ and $(Y,D_Y)$, and a positive integer $d$. The objective is to determine whether there is an embedding $F:X \rightarrow Y$ such that $d_{F} \leq d$, where $d_{F}$…
Given a network, the critical node detection problem finds a subset of nodes whose removal disrupts the network connectivity. Since many real-world systems are naturally modeled as graphs, assessing the vulnerability of the network is…
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…
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…
This work presents a two-stage neural architecture for learning and refining structural correspondences between graphs. First, we use localized node embeddings computed by a graph neural network to obtain an initial ranking of soft…
We study the maximum matching problem in fully dynamic graphs: a graph is undergoing both edge insertions and deletions, and the goal is to efficiently maintain a large matching after each edge update. This problem has received considerable…
Approximate solutions to various NP-hard combinatorial optimization problems have been found by learned heuristics using complex learning models. In particular, vertex (node) classification in graphs has been a helpful method towards…
In this paper, a new information theoretic framework for graph matching is introduced. Using this framework, the graph isomorphism and seeded graph matching problems are studied. The maximum degree algorithm for graph isomorphism is…
Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and…
Graph pattern matching algorithms to handle million-scale dynamic graphs are widely used in many applications such as social network analytics and suspicious transaction detections from financial networks. On the other hand, the computation…
This paper presents a simple and efficient approach for finding the bridges and failure points in a densely connected network mapped as a graph. The algorithm presented here is a parallel algorithm which works in a distributed environment.…
A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and…
Network alignment generalizes and unifies several approaches for forming a matching or alignment between the vertices of two graphs. We study a mathematical programming framework for network alignment problem and a sparse variation of it…
This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding…
Finding the shortest path between two points in a graph is a fundamental problem that has been well-studied over the past several decades. Shortest path algorithms are commonly applied to modern navigation systems, so our study aims to…
Many problems such as node classification and link prediction in network data can be solved using graph embeddings. However, it is difficult to use graphs to capture non-binary relations such as communities of nodes. These kinds of complex…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…