Academic literature on the topic 'Subgraph matching'

Continuous subgraph matching problem on dynamic graph has become a popular research topic in the field of graph analysis, which has a wide range of applications including information retrieval and community detection. Specifically, given a query graph q , an initial graph G 0 , and a graph update stream △ G i , the problem of continuous subgraph matching is to sequentially conduct all possible isomorphic subgraphs covering △ G i of q on G i (= G 0 ⊕ △ G i ). Since knowledge graph is a directed labeled multigraph having multiple edges between a pair of vertices, it brings new challenges for the problem focusing on dynamic knowledge graph. One challenge is that the multigraph characteristic of knowledge graph intensifies the complexity of candidate calculation, which is the combination of complex topological and attributed structures. Another challenge is that the isomorphic subgraphs covering a given region are conducted on a huge search space of seed candidates, which causes a lot of time consumption for searching the unpromising candidates. To address these challenges, a method of subgraph-indexed sequential subdivision is proposed to accelerating the continuous subgraph matching on dynamic knowledge graph. Firstly, a flow graph index is proposed to arrange the search space of seed candidates in topological knowledge graph and an adjacent index is designed to accelerate the identification of candidate activation states in attributed knowledge graph. Secondly, the sequential subdivision of flow graph index and the transition state model are employed to incrementally conduct subgraph matching and maintain the regional influence of changed candidates, respectively. Finally, extensive empirical studies on real and synthetic graphs demonstrate that our techniques outperform the state-of-the-art algorithms.

A subgraph H of a graph G with perfect matching is nice if G−V(H) has perfect matching. It is well-known that all fullerene graphs have perfect matchings and that all fullerene graphs contain some small connected graphs as nice subgraphs. In this contribution, we consider fullerene graphs arising from smaller fullerenes via the leapfrog transformation, and show that in such graphs, each pair of (necessarily disjoint) pentagons is nice. That answers in affirmative a question posed in a recent paper on nice pairs of odd cycles in fullerene graphs.

Graph data structure has been widely used across many application areas, such as web data, social network, and cheminformatics. The main benefit of storing data as graphs is there exists a rich set of graph algorithms and operations that can be used to solve various computing problems, including pattern matching, data mining, and image processing. Among these graph algorithms, the subgraph isomorphism problem is one of the most fundamental algorithms that can be utilized by many higher level applications. The subgraph isomorphism problem is defined as, given two graphs [Formula: see text] and [Formula: see text], whether [Formula: see text] contains a subgraph that is isomorphic to [Formula: see text]. In this paper, we consider a special case of the subgraph isomorphism problem called the subgraph matching problem, which tests whether [Formula: see text] is a subgraph of [Formula: see text]. We propose a protocol that solve the subgraph matching problem in a privacy-preserving manner. The protocol allows two parties to jointly compute whether one graph is a subgraph of the other, while protecting the private information about the input graphs. The protocol is secure under the semi-honest setting, where each party performs the protocol faithfully.

Interesting subgraph query aims to find subgraphs that are isomorphic to the given query graph from a data graph and rank the subgraphs according to their interestingness scores. However, the existing subgraph query approaches are inefficient when dealing with large-scale labeled data graph. This is caused by the following problems: (i) the existing work mainly focuses on unweighted query graphs, while ignoring the impact of query constraints on query results. (ii) Excessive number of subgraph candidates or complex joins between nodes in the subgraph candidates reduce the query efficiency. To solve these problems, this paper proposes an intelligent solution. Firstly, an Isotype Structure Graph Compression (ISGC) strategy is proposed to compress similar nodes in a graph to reduce the size of the graph and avoid unnecessary matching. Then, an auxiliary data structure Supergraph Topology Feature Index (STFIndex) is designed to replace the storage of the original data graph and improve the efficiency of an online query. After that, a partition method based on Edge Label Step Value (ELSV) is proposed to partition the index logically. In addition, a novel Top-K interest subgraph query approach is proposed, which consists of the multidimensional filtering (MDF) strategy, upper bound value (UBV) (Size-c) matching, and the optimizational join (QJ) method to filter out as many false subgraph candidates as possible to achieve fast joins. We conduct experiments on real and synthetic datasets. Experimental results show that the average performance of our approach is 1.35 higher than that of the state-of-the-art approaches when the query graph is unweighted, and the average performance of our approach is 2.88 higher than that of the state-of-the-art approaches when the query graph is weighted.

Himesis is a complete yet minimal kernel for meta-modelling and model transformation, which consists of a specification of hierarchical graphs and in a highly efficient matching algorithm. Himesis graphs encode the essence of models: nodes, edges, containment, attributes, names and labels. There is a defined set of events which transform the graphs. Above all Himesis introduces an explicit notion of hierarchy, which allows the specification of formalisms which were very hard to meta-model in the past, such as graph grammars. Moreover, with containment, it is possible to couple and reuse existing formalisms.
Himesis implements HVF, a new matching algorithm based on the VF2 approach. HVF extends VF2 with hierarchy and with several optimization strategies. It was designed to support advanced features that are required for graph rewriting, such as matching from a context as well as negative application conditions. We show that HVF is a faster algorithm than VF2 for matching of flat graphs. HVF is particularly efficient when matching irregular graphs.

Existeix un ressorgiment en l'ús de mètodes estructurals per al problema de reconeixement i recuperació per contingut d'objectes en imatges. La teoria de grafs, en particular, la posada en correspondència de grafs (graph matching) juga un paper rellevant en aixó. En particular, la detecció d'un objecte (o una part) en una imatge es pot formular com un aparellament de subgrafs en termes de característiques estructurals. El matching de subgrafs és una tasca difícil. Especialment a causa de la presència de valors atípics, molts dels algoritmes existents per al matching de grafs tenen di- ficultats en l'escenari de matching de subgrafs. A més, l'aparellament de subgrafs de manera exacta s'ha demostrat ser una problema NP-complet. Així que hi ha una activitat intensa a la comunitat cientíca per proporcionar algoritmes eficaços per abordar el problema de manera suboptimal. La majoria d'ells treballen amb algoritmes aproximats que tracten d'obtenir una solució inexacta en forma aproximada. A més, el reconeixement habitualment ha de fer front a la distorsió. L'aparellament de subgrafs de manera inexacta consisteix a trobar el millor isomorfisme sota una mesura de similitud. Des del punt de vista teòric, aquesta tesi proposa algoritmes per a la solució al problema de l'aparellament de subgrafs de manera aproximada i inexacta. Des d'un punt de vista aplicat, aquesta tesi tracta el problema de la detecció de símbols en imatges de documents gràfics o dibuixos lineals (symbol spotting). Aquest és un problema ben conegut a la comunitat de reconeixement de gràfics. Es pot aplicar per a la indexació i classificació de documents sobre la base dels seus continguts. El caràcter estructural d'aquest tipus de documents motiva de forma natural la utilització d'una representació de grafs. Així el problema de detectar símbols en documents gràfics pot ser considerat com un problema d'aparellament de subgrafs. Els principals desaàments en aquest domini d'aplicació són el soroll i les distorsions que provenen de l'ús, la digitalització i la conversió de ràster a vectors d'aquests documents. A part que la visió per computador en l'actualitat no limita les aplicacions a un nombre limitat d'imatges. Així que el pas a l'escala i tractar un gran nombre d'imatges en el reconeixement de documents gràfics és un altre desaàment. En aquesta tesi, d'una banda, hem treballat en representacions de grafs eficients i robustes per solucionar el soroll i les distorsions dels documents. D'altra banda, hem treballat en diferents mètodes de matching de grafs per resoldre el problema de l'aparellament inexacte de subgrafs, que també sigui escalable davant d'un considerable nombre d'imatges. En primer lloc, es proposa un mètode per a detectar símbols mitjançant funcions de hash de subgrafs serialitzats. L'organització del graf una vegada factoritzat en subestructures comunes, que es poden organitzar en taules hash en funció de les similituds estructurals, i la serialització de les mateixes en estructures unidimensionals com ara camins, són dues aportacions d'aquesta part de la tesi. L'ús de les tècniques de hashing ajuda a reduir substancialment l'espai de cerca i accelera el procediment de la detecció. En segon lloc, presentem mecanismes de similitud contextual basades en la propagació basada en camins (walks) sobre el graf producte (tensor product graph). Aquestes similituds contextuals impliquen més informació d'ordre superior i més àble que les similituds locals. Utilitzem aquestes similituds d'ordre superior per formular l'aparellament de subgrafs com una problema de selecció de nodes i arestes al graf producte. En tercer lloc, proposem agrupament perceptual basat en convexitats per formar regions quasi convexes que elimina les limitacions de la representació tradicional dels grafs de regions per al reconeixement gràfic. En quart lloc, es proposa una representació de graf jeràrquic mitjançant la simplificació/correcció dels errors estructurals per crear un graf jeràrquic del graf de base. Aquests estructures de grafs jeràrquics s'integren en mètodes d'aparellament de grafs. A part d'aixó, en aquesta tesi hem proporcionat una comparació experimental general de tots els mètodes i alguns dels mètodes de l'estat de l'art. A més, també s'han proporcionat bases de dades d'experimentació.
Existe un resurgimiento en el uso de métodos estructurales para el problema de reconocimiento y recuperación por contenido de objetos en imágenes. La teoría de grafos, en particular la puesta en correspondencia de grafos (graph matching) juega un papel relevante en ello. Así, la detección de un objeto (o una parte) en una imagen se puede formular como un emparejamiento de subgrafos en términos de características estructurals. El matching de subgrafos es una tarea difícil. Especialmente debido a la presencia de valores atípicos, muchos de los algoritmos existentes para el matching de grafos tienen dificultades en el escenario de matching de subgrafos. Además, el apareamiento de subgrafos de manera exacta ha demostrado ser una problema NP-completo . Así que hay una actividad intensa en la comunidad científica para proporcionar algoritmos eficaces para abordar el problema de manera suboptimal. La mayoría de ellos trabajan con algoritmos aproximados que tratan de obtener una solución inexacta en forma aproximada. Además, el reconocimiento habitualmente debe hacer frente a la distorsión. El emparejamiento de subgrafos de manera inexacta consiste en encontrar el mejor isomorfismo bajo una medida de similitud. Desde el punto de vista teórico, esta tesis propone algoritmos para la solución al problema del emparejamiento de subgrafos de manera aproximada e inexacta. Desde un punto de vista aplicado, esta tesis trata el problema de la detección de símbolos en imágenes de documentos gráficos o dibujos lineales (symbol spotting). Este es un problema conocido en la comunidad de reconocimiento de gráficos. Se puede aplicar para la indexación y clasificación de documentos sobre la base de sus contenidos. El carácter estructural de este tipo de documentos motiva de forma natural la utilización de una representación de grafos. Así el problema de detectar símbolos en documentos gráficos puede ser considerado como un problema de apareamiento de subgrafos. Los principales desafiós en este dominio de aplicación son el ruido y las distorsiones que provienen del uso, la digitalización y la conversión de raster a vectores de estos documentos. Aparte de que la visión por computador en la actualidad no limita las aplicaciones a un número limitado de imágenes. Así que el paso a la escala y tratar un gran número de imágenes en el reconocimiento de documentos gráficos es otro desafió. En esta tesis, por una parte, hemos trabajado en representaciones de grafos efi- cientes y robustas para solucionar el ruido y las distorsiones de los documentos. Por otra parte, hemos trabajado en diferentes métodos de matching de grafos para resolver el problema del emparejamiento inexacto de subgrafos, que también sea escalable ante un considerable número de imágenes. En primer lugar, se propone un método para de tectar símbolos mediante funciones de hash de subgrafos serializados. La organización del grafo una vez factorizado en subestructuras comunes, que se pueden organizar en tablas hash en función de las similitudes estructurales, y la serialización de las mismas en estructuras unidimensionales como caminos, son dos aportaciones de esta parte de la tesis. El uso de las técnicas de hashing ayuda a reducir sustancialmente el espacio de búsqueda y acelera el procedimiento de la detección. En segundo lugar, presentamos mecanismos de similitud contextual basadas en la propagación basada en caminos (walks) sobre el grafo producto (tensor product graph). Estas similitudes contextuales implican más información de orden superior y más áble que las similitudes locales. Utilizamos estas similitudes de orden superior para formular el apareamiento de subgrafos como una problema de selección de nodos y aristas al grafo producto. En tercer lugar, proponemos agrupamiento perceptual basado en convexidades para formar regiones casi convexas que elimina las limitaciones de la representación tradicional de los grafos de regiones para el reconocimiento gráfico. En cuarto lugar, se propone una representación de grafo jerárquico mediante la simplificación/corrección de los errores estructurales para crear un grafo jerárquico del grafo de base. Estos estructuras de grafos jerárquicos integran en métodos de emparejamiento de grafos. Aparte de esto, en esta tesis hemos proporcionado una comparación experimental general de todos los métodos y algunos de los métodos del estado del arte. Además, también se han proporcionado bases de datos de experimentación.
There is a resurgence in the use of structural approaches in the usual object recognition and retrieval problem. Graph theory, in particular, graph matching plays a relevant role in that. Specifically, the detection of an object (or a part of that) in an image in terms of structural features can be formulated as a subgraph matching. Subgraph matching is a challenging task. Specially due to the presence of outliers most of the graph matching algorithms do not perform well in subgraph matching scenario. Also exact subgraph isomorphism has proven to be an NP-complete problem. So naturally, in graph matching community, there are lot of efiorts addressing the problem of subgraph matching within suboptimal bound. Most of them work with approximate algorithms that try to get an inexact solution in approximate way. In addition, usual recognition must cope with distortion. Inexact graph matching consists in finding the best isomorphism under a similarity measure. Theoretically this thesis proposes algorithms for solving subgraph matching in an approximate and inexact way. We consider the symbol spotting problem on graphical documents or line drawings from application point of view. This is a well known problem in the graphics recognition community. It can be further applied for indexing and classification of documents based on their contents. The structural nature of this kind of documents easily motivates one for giving a graph based representation. So the symbol spotting problem on graphical documents can be considered as a subgraph matching problem. The main challenges in this application domain is the noise and distortions that might come during the usage, digitalization and raster to vector conversion of those documents. Apart from that computer vision nowadays is not any more confined within a limited number of images. So dealing a huge number of images with graph based method is a further challenge. In this thesis, on one hand, we have worked on eficient and robust graph representation to cope with the noise and distortions coming from documents. On the other hand, we have worked on difierent graph based methods and framework to solve the subgraph matching problem in a better approximated way, which can also deal with considerable number of images. Firstly, we propose a symbol spotting method by hashing serialized subgraphs. Graph serialization allows to create factorized substructures such as graph paths, which can be organized in hash tables depending on the structural similarities of the serialized subgraphs. The involvement of hashing techniques helps to reduce the search space substantially and speeds up the spotting procedure. Secondly, we introduce contextual similarities based on the walk based propagation on tensor product graph. These contextual similarities involve higher order information and more reliable than pairwise similarities. We use these higher order similarities to formulate subgraph matching as a node and edge selection problem in the tensor product graph. Thirdly, we propose near convex grouping to form near convex region adjacency graph which eliminates the limitations of traditional region adjacency graph representation for graphic recognition. Fourthly, we propose a hierarchical graph representation by simplifying/correcting the structural errors to create a hierarchical graph of the base graph. Later these hierarchical graph structures are matched with some graph matching methods. Apart from that, in this thesis we have provided an overall experimental comparison of all the methods and some of the state-of-the-art methods. Furthermore, some dataset models have also been proposed.

Thesis(Ph.D.)--Case Western Reserve University, 2010
Title from PDF (viewed on 2010-04-12) Department of Electrical Engineering and Computer Science (EECS) Includes abstract Includes bibliographical references and appendices Available online via the OhioLINK ETD Center

Thesis (Master of Sciences)--Case Western Reserve University, 2010
Department of EECS - Computer and Information Sciences Title from PDF (viewed on 2010-05-25) Includes abstract Includes bibliographical references and appendices Available online via the OhioLINK ETD Center

The current Internet architecture presents a barrier to accommodate the vigorous arising demand for deploying new network services and applications. The next-generation architecture views the network virtualization as the gateway to overcome this limitation. Network virtualization promises to run efficiently and securely multiple dedicated virtual networks (VNs) over a shared physical infrastructure. Each VN is tailored to host a unique application based on the user’s preferences. This thesis addresses the problem of the efficient embedding of multiple VNs onto a shared substrate network (SN). The contribution of this thesis are twofold: First, a novel hierarchical SN management framework is proposed that efficiently selects the optimum VN mapping scheme for the requested VN from more than one proposed VN mapping candidates obtained in parallel. In order to accommodate the arbitrary architecture of the VNs, the proposed scheme divides the VN request into smaller subgraphs, and individually maps them on the SN using a variation of the exact subgraph matching techniques. Second, the physical resources pricing policy is introduced that is based on time-ofuse, that reflects the effect of resource congestion introduced by VN users. The preferences of the VN users are first represented through corresponding demand-utility functions that quantify the sensitivity of the applications hosted by the VNs to resource consumption and time-of-use. A novel model of time-varying VNs is presented, where users are allowed to up- or down-scale the requested resources to continuously maximize their utility while minimizing the VNs embedding cost. In contrast to existing solutions, the proposed work does not impose any limitations on the size or topology of the VN requests. Instead, the search is customized according to the VN size and the associated utility. Extensive simulations are then conducted to demonstrate the improvement achieved through the proposed work in terms of network utilization, the ratio of accepted VN requests and the SP profits.

在大數據圖中進行子圖匹配查詢有著廣泛的應用。最近的研究表明，由於返回的匹配子圖的數量規模可能十分大，因此選取k 個最具多樣性的結果是十分有用並重要的。
論文著重研究了如何選取k 個最具多樣性的子圖查詢，即給定一個查詢圖，在大數據圖中返回k 個匹配子圖，使得它們所覆蓋的頂店數目最多。論文提出了一個基於重疊層數的新穎算法，該算法具有提前終止條件，並有近似比的下界保證。文章選取了常用的真實數據集對算法進行了實驗驗證，能夠一台普通的機器上以毫秒級的速度返回近似最優解。
Subgraph querying in a large data graph is interesting for different applications. A recent study shows that top-k diversified results are useful since the number of matching subgraphs can be very large.
In this work, we study the problem of top-k diversified subgraph querying that asks for a set of up to k subgraphs isomorphic to a given query graph, and that covers the largest number of vertices. We propose a novel levelbased algorithm for this problem which supports early termination and has a theoretical approximation guarantee. From experiments, most of our results on real datasets used in previous works are near optimal with a query time within 10ms on a commodity machine.
Yang, Zhengwei.
Thesis M.Phil. Chinese University of Hong Kong 2016.
Includes bibliographical references (leaves ).
Abstracts also in Chinese.
Title from PDF title page (viewed on …).
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.

Activity retrieval is a growing field in electrical engineering that specializes in the search and retrieval of relevant activities and events in video corpora. With the affordability and popularity of cameras for government, personal and retail use, the quantity of available video data is rapidly outscaling our ability to reason over it. Towards the end of empowering users to navigate and interact with the contents of these video corpora, we propose a framework for exploratory search that emphasizes activity structure and search space reduction over complex feature representations. Exploratory search is a user driven process wherein a person provides a system with a query describing the activity, event, or object he is interested in finding. Typically, this description takes the implicit form of one or more exemplar videos, but it can also involve an explicit description. The system returns candidate matches, followed by query refinement and iteration. System performance is judged by the run-time of the system and the precision/recall curve of of the query matches returned. Scaling is one of the primary challenges in video search. From vast web-video archives like youtube (1 billion videos and counting) to the 30 million active surveillance cameras shooting an estimated 4 billion hours of footage every week in the United States, trying to find a set of matches can be like looking for a needle in a haystack. Our goal is to create an efficient archival representation of video corpora that can be calculated in real-time as video streams in, and then enables a user to quickly get a set of results that match. First, we design a system for rapidly identifying simple queries in large-scale video corpora. Instead of focusing on feature design, our system focuses on the spatiotemporal relationships between those features as a means of disambiguating an activity of interest from background. We define a semantic feature vocabulary of concepts that are both readily extracted from video and easily understood by an operator. As data streams in, features are hashed to an inverted index and retrieved in constant time after the system is presented with a user's query. We take a zero-shot approach to exploratory search: the user manually assembles vocabulary elements like color, speed, size and type into a graph. Given that information, we perform an initial downsampling of the archived data, and design a novel dynamic programming approach based on genome-sequencing to search for similar patterns. Experimental results indicate that this approach outperforms other methods for detecting activities in surveillance video datasets. Second, we address the problem of representing complex activities that take place over long spans of space and time. Subgraph and graph matching methods have seen limited use in exploratory search because both problems are provably NP-hard. In this work, we render these problems computationally tractable by identifying the maximally discriminative spanning tree (MDST), and using dynamic programming to optimally reduce the archive data based on a custom algorithm for tree-matching in attributed relational graphs. We demonstrate the efficacy of this approach on popular surveillance video datasets in several modalities. Finally, we design an approach for successive search space reduction in subgraph matching problems. Given a query graph and archival data, our algorithm iteratively selects spanning trees from the query graph that optimize the expected search space reduction at each step until the archive converges. We use this approach to efficiently reason over video surveillance datasets, simulated data, as well as large graphs of protein data.

In this thesis, three generalizations of the matching problem are considered. The first problem is the existence of matrices with given row and column sums. This problem can be interpreted as the f-factor problem of a bipartite graph. The well-known existence theorem follows from maxfiow-mincut theorem, but it contains an exponential number (in the number of rows) of inequalities. We generalize the Gale-Ryser theorem and obtain some conditions under which this exponential number of inequalities can be reduced to a polynomial number of inequalities. The second problem is the general factor problem. Let G = (V, E) be a multigraph. An arbitrary subset BL, of {O, 1,2,. . . , deg(v)} is assigned to each vertex ʋ E Ʋ. We call a B-factor a spanning subgraph F of G such that deg (ʋ) ∈ Bv for every vertex ʋ ∈ V. A set B is said to have a gap of length p ≥1 if there exists an integer k such that k+ 1,.•.,k+p ∉ Bv, and yet k,k+p+ 1 ∉ Bv. It’s known that the problem is NP-complete if we allow gaps of length more than one. We extend the algorithm of Cornuéjols for simple graphs and obtain a strongly polynomial algorithm for finding a B-factor when each Bv doesn’t have a gap of length 2 or more. A new augmenting walk that need not alternate is introduced. The third problem is the square-free two-factor problem. A square-free two-factor is a two-factor in which the cycles don’t have length 4, i.e. are not squares. We obtain an augmenting path theorem like Berge’s augmenting path theorem for a 1-matching. Also we obtain a polynomial algorithm for finding a square-free two-factor when the squares of G are vertex-disjoint.

Graph matching problems are well studied and bring great contributions to Graph Theory from both the theoretical and practical points of view. There are numerous studies for unrestricted and weighted/unweighted matchings. More recently, subgraph-restricted matchings have been proposed, which consider properties of the subgraph induced by the vertices of the matching. In this paper, we approach one of these new proposals, disconnected matching, which seeks to study maximum matching, such that the subgraph induced by the matching vertices is disconnected. We have described efficient algorithms to solve the problem for chordal graphs and block graphs based on a theoretical characterization.