scholarly journals Faster Scaling Algorithms for General Graph Matching Problems

1989 ◽  
Author(s):  
Harold N. Gabow ◽  
Robert E. Tarjan
Keyword(s):  
Graph Matching ◽  
Matching Problems ◽  
General Graph ◽  
Scaling Algorithms

scholarly journals Faster scaling algorithms for general graph matching problems

1991 ◽  
Vol 38 (4) ◽  
pp. 815-853 ◽  
Author(s):  
Harold N. Gabow ◽  
Robert E. Tarjan
Keyword(s):  
Graph Matching ◽  
Matching Problems ◽  
General Graph ◽  
Scaling Algorithms

scholarly journals Emparelhamentos Conexos

2020 ◽  
Author(s):  
Bruno P. Masquio ◽  
Paulo E. D. Pinto ◽  
Jayme L. Szwarcfiter
Keyword(s):  
Connected Graph ◽  
Graph Matching ◽  
Linear Time ◽  
Time Algorithm ◽  
Maximum Matching ◽  
Linear Time Algorithm ◽  
Induced Subgraphs ◽  
Matching Problems ◽  
General Graph ◽  
The One

Graph matching problems are well known and studied, in which we want to find sets of pairwise non-adjacent edges. Recently, there has been an interest in the study of matchings in which the induced subgraphs by the vertices of matchings are connected or disconnected. Although these problems are related to connectivity, the two problems are probably quite different, regarding their complexity. While the complexity of finding a maximum disconnected mat- ching is still unknown for a general graph, the one for connected matchings can be solved in polynomial time. Our contribution in this paper is a linear time algorithm to find a maximum connected matching of a general connected graph, given a general maximum matching as input.

Recognizing Topological Analogy in Semantic Network

2015 ◽  
Vol 24 (03) ◽  
pp. 1550006 ◽  
Author(s):  
Milan Trifunovic ◽  
Milos Stojkovic ◽  
Dragan Misic ◽  
Miroslav Trajanovic ◽  
Miodrag Manic
Keyword(s):  
Graph Matching ◽  
Semantic Network ◽  
Semantic Model ◽  
Input Graph ◽  
Matching Problems ◽  
Semantic Categorization ◽  
Maximum Common Subgraph ◽  
Oriented Structure ◽  
Node Labels

Recognizing topological analogy between the parts of semantic network seems to be very important step in the process of semantic categorization and interpretation of data that are embedded into the semantic network. Considering the semantic network as a set of graphs, recognition of topological analogy between the parts of semantic network can be treated as maximum common subgraph problem which falls in the group of exact graph matching problems. In this paper authors propose a new algorithm for maximum common subgraph detection aimed to a specific semantic network called Active Semantic Model (ASM). This semantic network can be represented as the set of labeled directed multigraphs with unique node labels. The structure of these graphs is specific because associations or edges are labeled with several attributes and some of them are related to nodes connected by edge. That kind of association-oriented structure enables associations or edges to play key role in the process of semantic categorization and interpretation of data. Furthermore, this kind of structure enables modeling semantic contexts in a form of semantically designated graphs (of associations). Proposed algorithm is capable of recognizing simultaneously maximum common subgraph of input graph and each of the graphs representing different contexts in ASM semantic network.

scholarly journals A method for feature matching in images using descriptor structures

2019 ◽  
Vol 43 (5) ◽  
pp. 810-817 ◽  
Author(s):  
A.A. Zakharov ◽  
A.L. Zhiznyakov ◽  
V.S. Titov
Keyword(s):  
Feature Matching ◽  
Graph Matching ◽  
Weighted Graph ◽  
Matrix Decomposition ◽  
Image Features ◽  
Eigenvalues And Eigenvectors ◽  
Matching Problems ◽  
Initial Stage ◽  
Plane Image ◽  
Image Pairs

A method of feature matching in images using descriptor structures is considered in the work. The descriptors in the developed method can be any known solutions in the field of computer vision. However, inaccuracies can occur when matching image pairs. It is proposed that descriptor structures should be compared to eliminate the “outliers”. Descriptor structures are described using graphs. An Umeyama method is used to find matching features using descriptor structures. The method is based on the decomposition of matrices into eigenvalues and eigenvectors for weighted graph matching problems. Thus, matches are based on the descriptor at the initial stage. Two graphs are then constructed for each image based on the resulting sets of mapped features. The weights of the graph are distances between all image features, calculated using the Gauss function. Weight matrices are built for each graph. Matrix decomposition is carried out into eigenvalues and eigenvectors. The resulting matrix is calculated based on the Umeyama method and correct matches are found. Thus, false matches are excluded from the set of matches obtained using descriptors by comparing structures. The method is invariant to zoom and in-plane image rotation. The method leads to correct results only if the number of correct matches is greater than the number of false matches. The complexity of the developed algorithm is proportional to the number of matches found.

Optimization in Model Matching and Perceptual Organization

1989 ◽  
Vol 1 (2) ◽  
pp. 218-229 ◽  
Author(s):  
Eric Mjolsness ◽  
Gene Gindi ◽  
P. Anandan
Keyword(s):  
Perceptual Grouping ◽  
Graph Matching ◽  
Optimization Approach ◽  
Model Matching ◽  
Objective Functions ◽  
Levels Of Abstraction ◽  
Matching Problems ◽  
Inexact Graph Matching ◽  
Analog Neural Networks ◽  
Multiple Levels

We introduce an optimization approach for solving problems in computer vision that involve multiple levels of abstraction. Our objective functions include compositional and specialization hierarchies. We cast vision problems as inexact graph matching problems, formulate graph matching in terms of constrained optimization, and use analog neural networks to perform the optimization. The method is applicable to perceptual grouping and model matching. Preliminary experimental results are shown.

scholarly journals Dynamic Programming Bipartite Belief Propagation For Hyper Graph Matching

2017 ◽  
Author(s):  
Zhen Zhang ◽  
Julian McAuley ◽  
Yong Li ◽  
Wei Wei ◽  
Yanning Zhang ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Graphical Models ◽  
Belief Propagation ◽  
Graph Matching ◽  
Matching Problem ◽  
Bipartite Matching ◽  
Matching Problems ◽  
Inference Problems ◽  
Order Relations ◽  
Traditional Approaches

Hyper graph matching problems have drawn attention recently due to their ability to embed higher order relations between nodes. In this paper, we formulate hyper graph matching problems as constrained MAP inference problems in graphical models. Whereas previous discrete approaches introduce several global correspondence vectors, we introduce only one global correspondence vector, but several local correspondence vectors. This allows us to decompose the problem into a (linear) bipartite matching problem and several belief propagation sub-problems. Bipartite matching can be solved by traditional approaches, while the belief propagation sub-problem is further decomposed as two sub-problems with optimal substructure. Then a newly proposed dynamic programming procedure is used to solve the belief propagation sub-problem. Experiments show that the proposed methods outperform state-of-the-art techniques for hyper graph matching.

scholarly journals A NOVEL APPROACH FOR PART BASED OBJECT MATCHING USING DISTANCE METRIC LEARNING WITH GRAPH CONVOLUTIONAL NETWORKS

2021 ◽  
Vol XLIV-2/W1-2021 ◽  
pp. 149-154
Author(s):  
V. Kozlov ◽  
A. Maysuradze
Keyword(s):  
Object Representation ◽  
Graph Matching ◽  
Quadratic Assignment Problem ◽  
Metric Learning ◽  
Quadratic Assignment ◽  
Distance Metric ◽  
Matching Problem ◽  
Matching Problems ◽  
Convolutional Networks ◽  
Novel Approach

Abstract. Part-based object representation and part matching problem often appear in various areas of data analysis. A special case of particular interest is when parts are not fully separated, but in relations with each other. The natural way to model such objects are graphs, and part matching problem becomes graph matching problem. Over the years, many methods to solve graph matching problems have been proposed, but it remains relevant due to its complexity. We propose a novel approach to solving graph matching problem based on learning distance metric on graph vertices. We empirically demonstrate that our method outperforms traditional methods based on solving quadratic assignment problem. We also provide an theoretical estimation of computational complexity of proposed method.

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