• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.6
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• pp.2986-2999
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• 2019

The uncertainties of the uncertain graph make the traditional definition and algorithms on mining dense graph for certain graph not applicable. The subgraph obtained by maximizing expected density from an uncertain graph always has many low edge-probability data, which makes it low reliable and low expected edge density. Based on the concept of ${\beta}$-subgraph, to overcome the low reliability of the densest subgraph, the concept of optimal ${\beta}$-subgraph is proposed. An efficient greedy algorithm is also developed to find the optimal ${\beta}$-subgraph. Simulation experiments of multiple sets of datasets show that the average edge-possibility of optimal ${\beta}$-subgraph is improved by nearly 40%, and the expected edge density reaches 0.9 on average. The parameter ${\beta}$ is scalable and applicable to multiple scenarios.

• KIPS Transactions on Software and Data Engineering
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• v.3 no.3
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• pp.119-124
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• 2014

Let G = (V, E) be a graph. Maximum Bipartite Subgraph Problem is to convert a graph G into a bipartite graph by removing minimum number of edges. This problem belongs to NP-complete; hence, in this research, we are suggesting a new metaheuristic algorithm which combines Tabu search and GRASP.

• The Journal of the Korea Contents Association
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• v.20 no.8
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• pp.42-53
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• 2020

With the development of social network services, graph structures have been utilized to represent relationships among objects in various applications. Recently, a demand of subgraph matching in real-time graph streams has been increased. Therefore, an efficient approximate Top-k subgraph matching scheme for low latency in real-time graph streams is required. In this paper, we propose an approximate Top-k subgraph matching scheme considering data reuse in graph stream environments. The proposed scheme utilizes the distributed stream processing platform, called Storm to handle a large amount of stream data. We also utilize an existing data reuse scheme to decrease stream processing costs. We propose a distance based summary indexing technique to generate Top-k subgraph matching results. The proposed summary indexing technique costs very low since it only stores distances among vertices that are selected in advance. Finally, we provide k subgraph matching results to users by performing an approximate Top-k matching on the summary indexing. In order to show the superiority of the proposed scheme, we conduct various performance evaluations in diverse real world datasets.

• The Journal of the Korea Contents Association
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• v.22 no.8
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• pp.33-43
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• 2022

Labeled graphs are used to represent entities, their relationships, and their structures in real data such as knowledge graphs and protein interactions. With the rapid development of IT and the explosive increase in data, there has been a need for a subgraph matching technology to provide information that the user is interested in. In this paper, we propose an approximate Top-k labeled subgraph matching scheme that considers the semantic similarity of labels and the difference in graph structure. The proposed scheme utilizes a learning model using FastText in order to consider the semantic similarity of a label. In addition, the label similarity graph(LSG) is used for approximate subgraph matching by calculating similarity values between labels in advance. Through the LSG, we can resolve the limitations of the existing schemes that subgraph expansion is possible only if the labels match exactly. It supports structural similarity for a query graph by performing searches up to 2-hop. Based on the similarity value, we provide k subgraph matching results. We conduct various performance evaluations in order to show the superiority of the proposed scheme.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.155-167
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• 2007

A graph G is called to be a 2-degree integral subgraph of a q-tree if it is obtained by deleting an edge e from an integral subgraph that is contained in exactly q - 1 triangles. An added-vertex q-tree G with n vertices is obtained by taking two vertices u, v (u, v are not adjacent) in a q-trees T with n - 1 vertices such that their intersection of neighborhoods of u, v forms a complete graph $K_{q}$, and adding a new vertex x, new edges xu, xv, $xv_{1},\;xv_{2},\;{\cdots},\;xv_{q-4}$, where $\{v_{1},\;v_{2},\;{\cdots},\;v_{q-4}\}\;{\subseteq}\;K_{q}$. In this paper we prove that a graph G with minimum degree not equal to q - 3 and chromatic polynomial $$P(G;{\lambda})\;=\;{\lambda}({\lambda}-1)\;{\cdots}\;({\lambda}-q+2)({\lambda}-q+1)^{3}({\lambda}-q)^{n-q-2}$$ with $n\;{\geq}\;q+2$ has and only has 2-degree integral subgraph of q-tree with n vertices and added-vertex q-tree with n vertices.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.2
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• pp.375-382
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• 1996

In this paper, aneffective method for computing source to terminal reliability of network by decomposition is described. A graph is modeled after a network, and decomposed into two subgraphs. A logic product term of one subgraph is computed, and a graph of the other subgraphs is made according to the event representing the logic product term, and it's logic product term is compted. By multiplying the logic product term of one subgraph by that of the other subgraphs, a method for computing the source to terminal reliability is proposed. the time complexity for computing all the logic product terms of one subgraph is the product of copies of the number of edges in the subgraph of 2, and that of the other subgraph is the number of edges multiplied by the number of logic product terms. This method requires less computation time than that not by decomposition.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.3 no.1
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• pp.185-196
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• 1999

In this dissertation, a new off-line recognition system is proposed using a subgraph pattern, neural network. After thinning is applied to input characters, balance having a noise elimination function on location is performed. Then as the first step for recognition procedure, circular elements are extracted and recognized. From the subblock HT, space feature points such as endpoint, flex point, bridge point are extracted and a subgraph pattern is formed observing the relations among them. A region where vowel can exist is allocated and a candidate point of the vowel is extracted. Then, using the subgraph pattern dictionary, a vowel is recognized. A same method is applied to extract horizontal vowels and the vowel is recognized through a simple structural analysis. For verification of recognition subgraph in this paper, experiments are done with the most frequently used Myngjo font, Gothic font for printed characters and handwritten characters. In case of Gothic font, character recognition rate was 98.9%. For Myngjo font characters, the recognition rate was 98.2%. For handwritten characters, the recognition rate was 92.5%. The total recognition rate was 94.8% with mixed handwriting and printing characters for multi-font recognition.

• Journal of the Korea Society of Computer and Information
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• v.21 no.12
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• pp.1-10
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• 2016

In this paper, we attempt to prevent certain cases by tracing a history and making genogram about open source software and its modification using similarity of source code. There are many areas which use open source software actively and widely, and open source software contributes their development. However, there are many unconscious cases like ignoring license or intellectual properties infringe which can lead litigation. To prevent such situation, we analyze source code similarity using program dependence graph which resembles subgraph isomorphism problem, a typical NP-complete problem. To solve subgraph isomorphism problem, we utilized harmony search of metaheuristic algorithm and compared its result with a genetic algorithm. For the future works, we represent open source software as program dependence graph and analyze their similarity.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1199-1210
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• 2019

In this paper, we consider a class of inhomogeneous random intersection graphs by assigning random weight to each vertex and two vertices are adjacent if they choose some common elements. In the inhomogeneous random intersection graph model, vertices with larger weights are more likely to acquire many elements. We show the Poisson convergence of the number of induced copies of a fixed subgraph as the number of vertices n and the number of elements m, scaling as $m={\lfloor}{\beta}n^{\alpha}{\rfloor}$ (${\alpha},{\beta}>0$), tend to infinity.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2005.09a
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• pp.267-271
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• 2005

The goal of data mining is to extract new and useful knowledge from large scale datasets. As the amount of available data grows explosively, it became vitally important to develop faster data mining algorithms for various types of data. Recently, an interest in developing data mining algorithms that operate on graphs has been increased. Especially, mining frequent patterns from structured data such as graphs has been concerned by many research groups. A graph is a highly adaptable representation scheme that used in many domains including chemistry, bioinformatics and physics. For example, the chemical structure of a given substance can be modelled by an undirected labelled graph in which each node corresponds to an atom and each edge corresponds to a chemical bond between atoms. Internet can also be modelled as a directed graph in which each node corresponds to an web site and each edge corresponds to a hypertext link between web sites. Notably in bioinformatics area, various kinds of newly discovered data such as gene regulation networks or protein interaction networks could be modelled as graphs. There have been a number of attempts to find useful knowledge from these graph structured data. One of the most powerful analysis tool for graph structured data is frequent subgraph analysis. Recurring patterns in graph data can provide incomparable insights into that graph data. However, to find recurring subgraphs is extremely expensive in computational side. At the core of the problem, there are two computationally challenging problems. 1) Subgraph isomorphism and 2) Enumeration of subgraphs. Problems related to the former are subgraph isomorphism problem (Is graph A contains graph B?) and graph isomorphism problem(Are two graphs A and B the same or not?). Even these simplified versions of the subgraph mining problem are known to be NP-complete or Polymorphism-complete and no polynomial time algorithm has been existed so far. The later is also a difficult problem. We should generate all of 2$^n$ subgraphs if there is no constraint where n is the number of vertices of the input graph. In order to find frequent subgraphs from larger graph database, it is essential to give appropriate constraint to the subgraphs to find. Most of the current approaches are focus on the frequencies of a subgraph: the higher the frequency of a graph is, the more attentions should be given to that graph. Recently, several algorithms which use level by level approaches to find frequent subgraphs have been developed. Some of the recently emerging applications suggest that other constraints such as connectivity also could be useful in mining subgraphs : more strongly connected parts of a graph are more informative. If we restrict the set of subgraphs to mine to more strongly connected parts, its computational complexity could be decreased significantly. In this paper, we present an efficient algorithm to mine frequent subgraphs that are more strongly connected. Experimental study shows that the algorithm is scaling to larger graphs which have more than ten thousand vertices.