Modern search engines answer keyword-based queries extremely efficiently. The impressive speed is due to clever inverted index structures, caching, a domain-independent knowledge of strings, and thousands of machines. Several research efforts have attempted to generalize keyword search to keytree and keygraph searching, because trees and graphs have many applications in next-generation database systems. This paper surveys both algorithms and applications, giving some emphasis to our own work.

Abstract—This paper describes a Bayesian framework for performing relational graph matching by discrete relaxation. Our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching. Broadly speaking there are two main aspects to this study. Firstly we focus on the issue of how relational inexactness may be quantified. We illustrate that several popular relational distance measures can be recovered as specific limiting cases of the Bayesian consistency measure. The second aspect of our comparison concerns the way in which structural inexactness is controlled. We investigate three different realizations of the matching process which draw on contrasting control models. The main conclusion of our study is that the active process of graph-editing outperforms the alternatives in terms of its ability to effectively control a large population of contaminating clutter.

AbstractÐThis paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is to say, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions. Commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm. Our second contribution is to cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows us to efficiently recover correspondence matches using singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding methods. Index TermsÐInexact graph matching, EM algorithm, matrix factorization, mixture models, Delaunay triangulations. 1

AbstractÐThis paper describes a novel framework for comparing and matching corrupted relational graphs. The paper develops the idea of edit-distance originally introduced for graph-matching by Sanfeliu and Fu [1]. We show how the Levenshtein distance can be used to model the probability distribution for structural errors in the graph-matching problem. This probability distribution is used to locate matches using MAP label updates. We compare the resulting graph-matching algorithm with that recently reported by Wilson and Hancock. The use of edit-distance offers an elegant alternative to the exhaustive compilation of label dictionaries. Moreover, the method is polynomial rather than exponential in its worst-case complexity. We support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem. This demonstrates experimentally that the gain in efficiency is not at the expense of quality of match.

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Hierarchical image structures are abundant in computer vision and have been used to encode part structure, scale spaces, and a variety of multiresolution features. In this paper, we describe a framework for indexing such representations that embeds the topological structure of a directed acyclic graph (DAG) into a low-dimensional vector space. Based on a novel spectral characterization of a DAG, this topological signature allows us to efficiently retrieve a promising set of candidates from a database of models using a simple nearest-neighbor search. We establish the insensitivity of the signature to minor perturbation of graph structure due to noise, occlusion, or node split/merge. To accommodate large-scale occlusion, the DAG rooted at each nonleaf node of the query "votes" for model objects that share that "part," effectively accumulating local evidence in a model DAG's topological subspaces. We demonstrate the approach with a series of indexing experiments in the domain of view-based 3D object recognition using shock graphs.

A~s~Qc~-A method for the recognition of multifont printed characters is proposed, giving emphasis to the identification of structural descriptions of character shapes using prototypes. Noise and shape variations are modeled as series of transformations from groups of features in the data to features in each prototype. Thus, the method manages systematically the relative distortion between a candidate shape and its prototype, accomplishing robustness to noise with less than two prototypes per class, on average. Our method uses a flexible matching between components and a flexible grouping of the individual components to be matched. A number of shape transformations are defined, including filling of gaps, so that the method handles broken characters. Also, a measure of the amount of distortion that these transformations cause is given. Classification of character shapes is defined as a minimization problem among the possible transformations that map an input shape into prototypical shapes. Some tests with hand-printed numerals confirmed the method’s high robustness level. Zndex Terms-Shape distance, graph matching, relative neighborhood graph, broken character recognition, subgraph homeomorphism. I.

Abstract—This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix. We pose the problem of graph-matching as a maximum a posteriori probability (MAP) alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability. We compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice. The edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched. We demonstrate the utility of the edit distance on a number of graph clustering problems. Index Terms—Graph edit distance, graph seriation, maximum a posteriori probability (MAP), graph-spectral methods. 1

Comparative analysis of metabolic pathways in different genomes can give insights into the understanding of evolutionary and organizational relationships among species. This type of analysis allows one to measure the evolution of complete processes (with different functional roles) rather than the individual elements of a conventional analysis. We present a new technique for the phylogenetic analysis of metabolic pathways based on the topology of the underlying graphs. A distance measure between graphs is defined using the similarity between nodes of the graphs and the structural relationship between them.

Objects like road networks, CAD/CAM components, electrical or electronic circuits, molecules, can be represented as graphs, in many modern applications. In this paper, we propose an efficient and effective graph manipulation technique that can be used in graph-based similarity search. Given a query graph G q (V; E), we would like to determine fast which are the graphs in the database that are similar to G q (V; E), with respect to a similarity measure. First, we study the similarity measure between two graphs. Then, we discuss graph representation techniques by means of multidimensional vectors. It is shown that no false dismissals are introduced by using the vector representation. Finally we illustrate some representative queries that can be handled by our approach, and present experimental results, based on the proposed graph similarity algorithm. The results show that considerable savings are obtained with respect to computational effort and I/O operations, in comparison to conventional searching techniques.