Subgraph Matching Using Graph Neural Network

Subgraph matching problem is identifying a target subgraph in a graph. Graph neural network (GNN) is an artificial neural network model which is capable of processing general types of graph structured data. A graph may contain many subgraphs isomorphic to a given target graph. In this paper GNN is modeled to identify a subgraph that matches the target graph along with its characteristics. The simulation results show that GNN is capable of identifying a target sub-graph in a graph.

Perfect 1-k Matchings of Bipartite Graphs

Let k be a positive integer and G a bipartite graph with bipartition (X,Y). A perfect 1-k matching is an edge subset M of G such that each vertex in Y is incident with exactly one edge in M and each vertex in X is incident with exactly k edges in M. A perfect 1-k matching is an optimal semi-matching related to the load-balancing problem, where a semi-matching is an edge subset M such that each vertex in Y is incident with exactly one edge in M, and a vertex in X can be incident with an arbitrary number of edges in M. In this paper, we give three sufficient and necessary conditions for the existence of perfect 1-k matchings and for the existence of 1-k matchings covering | X |−dvertices in X, respectively, and characterize k-elementary bipartite graph which is a graph such that the subgraph induced by all k-allowed edges is connected, where an edge is k-allowed if it is contained in a perfect 1-k matching.

Matching spatial relation graphs using a constrained partial permutation strategy

A constrained partial permutation strategy is proposed for matching spatial relation graph (SRG), which is used in our sketch input and recognition system Smart Sketchpad for representing the spatial relationship among the components of a graphic object. Using two kinds of matching constraints dynamically generated in the matching process, the proposed approach can prune most improper mappings between SRGs during the matching process. According to our theoretical analysis in this paper, the time complexity of our approach is O(n 2) in the best case, and O(n!) in the worst case, which occurs infrequently. The spatial complexity is always O(n) for all cases. Implemented in Smart Sketchpad, our proposed strategy is of good performance.

Inexact graph matching using a hierarchy of matching processes

Inexact graph matching algorithms have proved to be useful in many applications,such as character recognition,shape analysis,and image analysis. Inexact graph matching is,however,inherently an NP-hard problem with exponential computational complexity. Much of the previous research has focused on solving this problem using heuristics or estimations. Unfortunately,many of these techniques do not guarantee that an optimal solution will be found. It is the aim of the proposed algorithm to reduce the complexity of the inexact graph matching process,while still producing an optimal solution for a known application. This is achieved by greatly simplifying each individual matching process,and compensating for lost robustness by producing a hierarchy of matching processes. The creation of each matching process in the hierarchy is driven by an application-specific criterion that operates at the subgraph scale. To our knowledge,this problem has never before been approached in this manner. Results show that the proposed algorithm is faster than two existing methods based on graph edit operations.The proposed algorithm produces accurate results in terms of matching graphs,and shows promise for the application of shape matching. The proposed algorithm can easily be extended to produce a sub-optimal solution if required.

Exact Graph Pattern Matching:Applications,Progress and Prospects

Graph pattern matching(GPM)can be used to mine the key information in graphs.Exact GPM is one of the most commonly used methods among all the GPM-related methods,which aims to exactly find all subgraphs for a given query graph in a data graph.The exact GPM has been widely used in biological data analyses,social network analyses and other fields.In this paper,the applications of the exact GPM were first introduced,and the research progress of the exact GPM was summarized.Then,the related algorithms were introduced in detail,and the experiments on the state-of-the-art exact GPM algorithms were conducted to compare their performance.Based on the experimental results,the applicable scenarios of the algorithms were pointed out.New research opportunities in this area were proposed.

Multi-scale Graph-matching Based Kernel for Character Recognition from Natural Scenes

认出从自然景色图象提取的字符由于 intraclass 变化的高度是相当挑战性的。在这份报纸，我们为景色特性识别建议一个多尺度的匹配图的基于的核。以便捕获人物的内在地特殊的结构，每幅图象被与多尺度的图象格子联系的几张图代表。当也越过邻近的节点保存空间一致性时，二幅图象的类似被匹配二张图(图象) 因此定义为最佳精力，它在图为每个节点发现最好的火柴。计算类似是合适的为支持向量机器(SVM ) 构造一个核。与多尺度的格子匹配图获得的多重核被联合以便最后的核是更柔韧的。挑战性的 Chars74k 和 ICDAR03-CH 数据集上的试验性的结果证明建议方法比现状方法更好表现。

A Novel Symbolic Algorithm for Maximum Weighted Matching in Bipartite Graphs

The maximum weighted matching problem in bipartite graphs is one of the classic combinatorial optimization problems, and arises in many different applications. Ordered binary decision diagram (OBDD) or algebraic decision diagram (ADD) or variants thereof provides canonical forms to represent and manipulate Boolean functions and pseudo-Boolean functions efficiently. ADD and OBDD-based symbolic algorithms give improved results for large-scale combinatorial optimization problems by searching nodes and edges implicitly. We present novel symbolic ADD formulation and algorithm for maximum weighted matching in bipartite graphs. The symbolic algorithm implements the Hungarian algorithm in the context of ADD and OBDD formulation and manipulations. It begins by setting feasible labelings of nodes and then iterates through a sequence of phases. Each phase is divided into two stages. The first stage is building equality bipartite graphs, and the second one is finding maximum cardinality matching in equality bipartite graph. The second stage iterates through the following steps: greedily searching initial matching, building layered network, backward traversing node-disjoint augmenting paths, updating cardinality matching and building residual network. The symbolic algorithm does not require explicit enumeration of the nodes and edges, and therefore can handle many complex executions in each step. Simulation experiments indicate that symbolic algorithm is competitive with traditional algorithms.

ENTIRE CHROMATIC NUMBER AND Δ-MATCHING OF OUTERPLANE GRAPHS

Let G be an outerplane graph with maximum degree A and the entire chromatic number Xvef（G）. This paper proves that if △ ≥6, then △＋ 1≤Xvef（G）≤△＋ 2, and Xvef （G） = △＋ 1 if and only if G has a matching M consisting of some inner edges which covers all its vertices of maximum degree.

The Matching Uniqueness of A Graphs

In the paper, We discussed the matching uniqueness of graphs with degree sequence . The necessary and sufficient conditions for and its complement are matching unique are given.

The Number of Matching Equivalent for the Union Graph of Vertices and Cycles

For two graphs G and H, if G and H have the same matching polynomial, then G and H are said to be matching equivalent. We denote by δ (G), the number of the matching equivalent graphs of G. In this paper, we give δ (sK1 ∪ t1C9 ∪ t2C15), which is a generation of the results of in [1].

K-Means Graph Database Clustering and Matching for Fingerprint Recognition

The graph can contain huge amount of data. It is heavily used for pattern recognition and matching tasks like symbol recognition, information retrieval, data mining etc. In all these applications, the objects or underlying data are represented in the form of graph and graph based matching is performed. The conventional algorithms of graph matching have higher complexity. This is because the most of the applications have large number of sub graphs and the matching of these sub graphs becomes computationally expensive. In this paper, we propose a graph based novel algorithm for fingerprint recognition. In our work we perform graph based clustering which reduces the computational complexity heavily. In our algorithm, we exploit structural features of the fingerprint for K-means clustering of the database. The proposed algorithm is evaluated using realtime fingerprint database and the simulation results show that our algorithm outperforms the existing algorithm for the same task.

Ordering of Unicyclic Graphs with Perfect Matchings by Minimal Matching Energies

In 2012, Gutman and Wagner proposed the concept of the matching energy of a graph and pointed out that its chemical applications can go back to the 1970s. The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. Let u and v be the non-isolated vertices of the graphs G and H with the same order, respectively. Let wi?be a non-isolated vertex of graph Gi?where i=1, 2, …, k. We use Gu(k)?(respectively, Hv(k)) to denote the graph which is the coalescence of G (respectively, H) and G1, G2,…, Gk?by identifying the vertices u (respectively, v) and w1, w2,…, wk. In this paper, we first present a new technique of directly comparing the matching energies of Gu(k)?and Hv(k), which can tackle some quasi-order incomparable problems. As the applications of the technique, then we can determine the unicyclic graphs with perfect matchings of order 2n with the first to the ninth smallest matching energies for all n≥211.

Graph Based Filtering and Matching for Symbol Recognition

Pattern recognition is a task of searching particular patterns or features in the given input. The data mining, computer networks, genetic engineering, chemical structure analysis, web services etc. are few rapidly growing applications where pattern recognition has been used. Graphs are very powerful model applied in various areas of computer science and engineering. This paper proposes a graph based algorithm for performing the graphical symbol recognition. In the proposed approach, a graph based filtering prior to the matching is performed which significantly reduces the computational complexity. The proposed algorithm is evaluated using a large number of input drawings and the simulation results show that the proposed algorithm outperforms the existing algorithms.

Efficient Stereo Matching Scheme Based on Graph Cuts

A new stereo matching scheme from image pairs based on graph cuts is given,which can solve the problem of large color differences as the result of fusing matching results of graph cuts from different color spaces.This scheme builds normalized histogram and reference histogram from matching results,and uses clustering algorithm to process the two histograms.Region histogram statistical method is adopted to retrieve depth data to achieve final matching results.Regular stereo matching library is used to verify this scheme,and experiments reported in this paper support availability of this method for automatic image processing.This scheme renounces the step of manual selection for adaptive color space and can obtain stable matching results.The whole procedure can be executed automatically and improve the integration level of image analysis process.

The Symbolic OBDD Algorithm for Finding Optimal Semi-matching in Bipartite Graphs

The optimal semi-matching problem is one relaxing form of the maximum cardinality matching problems in bipartite graphs, and finds its applications in load balancing. Ordered binary decision diagram (OBDD) is a canonical form to represent and manipulate Boolean functions efficiently. OBDD-based symbolic algorithms appear to give improved results for large-scale combinatorial optimization problems by searching nodes and edges implicitly. We present novel symbolic OBDD formulation and algorithm for the optimal semi-matching problem in bipartite graphs. The symbolic algorithm is initialized by heuristic searching initial matching and then iterates through generating residual network, building layered network, backward traversing node-disjoint augmenting paths, and updating semi-matching. It does not require explicit enumeration of the nodes and edges, and therefore can handle many complex executions in each step. Our simulations show that symbolic algorithm has better performance, especially on dense and large graphs.

Rainbow Matchings in Properly Colored Bipartite Graphs

Let G be a properly colored bipartite graph. A rainbow matching of G is such a matching in which no two edges have the same color. Let G be a properly colored bipartite graph with bipartition (X,Y) and . We show that if , then G has a rainbow coloring of size at least .

Solving the Maximum Matching Problem on Bipartite Star123-Free Graphs in Linear Time

The bipartite Star123-free graphs were introduced by V. Lozin in [1] to generalize some already known classes of bipartite graphs. In this paper, we extend to bipartite Star123-free graphs a linear time algorithm of J. L. Fouquet, V. Giakoumakis and J. M. Vanherpe for finding a maximum matching in bipartite Star123, P7-free graphs presented in [2]. Our algorithm is a solution of Lozin’s conjecture.

Some results on the Induced Matching Partition Number of Product Graphs

The induced matching partition number of graph G is the minimum integer k such that there exists a k-partition(V1,V2,…,Vk) of V(G)such that,for each i(1≤i≤k),G[Vi] is 1-regular.In this paper,we study the induced matching partition number of product graphs.We provide a lower bound and an upper bound for the induced matching partition number of product graphs,and exact results are given for some special product graphs.

基于知识图谱的不动产登记数据整合方法研究

不动产登记存量数据整合是不动产登记重要的支撑,由于不动产登记存量数据本身多源性和异构性的特点,使其难以准确地进行整合关联,因此数据整合关联成为不动产登记数据整合中的关键环节。利用地址坐落进行匹配是其常用的主要方法,现有的地址匹配方法仅从地址字段本身出发,很难建立精准的匹配关系。研究通过对传统标准的地址库进行地址分词,结合POI地址,构建不动产统一登记地址知识图谱,对不动产登记数据和权籍数据地址的特征提取和地址分类,从而实现不动产登记数据与权籍地址的匹配。实验表明,此方法能提高匹配的关联率和准确度,将此方法应用于广州市中心区不动产登记数据整合项目中,极大地提高了不动产数据整合的效率。

基于图的异构数据集成方法研究

企业各部门对数据施行分散管理,烟囱式的系统建设使数据散落在异构数据库中,异构数据给当前数据集成工作带来了系列挑战。为解决企业异构系统数据汇聚融合的问题,提出一种基于图的端到端的数据集成框架。首先,根据关系型数据模型的主外键关系将表和字段的实体关系构建成网络图,将表名和字段名称分别看作图中不同类型的实体。然后,将构建的图输入图神经网络,经过图卷积得到图中各节点的向量表征,基于节点向量可计算任意所需匹配的两个图的节点映射关系。完成图中表和字段的对齐后,再将不同字段值标准化,即将每个单元格的值映射为标准值。最后,将以上结果工程化为数据库可执行的查询语句,从而实现异构数据融合。在企业内部的真实数据上进行验证,实验结果表明,文中所提框架能提高数据集成的开发效率,且该模型不受业务领域限制,具有较强的移植性。