• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.175-190
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• 2019

In this paper, we provide results for the search number of the Cartesian product of graphs. We consider graphs on opposing ends of the spectrum: paths and cliques. Our main result determines the pathwidth of the product of cliques and provides a lower bound for the search number of the product of cliques. A consequence of this result is a bound for the search number of the product of arbitrary graphs G and H based on their respective clique numbers.

• Proceedings of the Korea Information Processing Society Conference
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• 2022.11a
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• pp.374-376
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• 2022

Community detection is meaningful research in social network analysis, and many existing studies use graph theory analysis methods to detect communities. This paper proposes a method to detect community by detecting maximal cliques and obtain the high influence cliques by high influence nodes, then merge the cliques with high similarity in social network.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.569-583
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• 2019

Given a graph G, the Motzkin and Straus formulation of the maximum clique problem is the quadratic program (QP) formed from the adjacent matrix of the graph G over the standard simplex. It is well-known that the global optimum value of this QP (called Lagrangian) corresponds to the clique number of a graph. It is useful in practice if similar results hold for hypergraphs. In this paper, we attempt to explore the relationship between the Lagrangian of a hypergraph and the order of its maximum cliques when the number of edges is in a certain range. Specifically, we obtain upper bounds for the Lagrangian of a hypergraph when the number of edges is in a certain range. These results further support a conjecture introduced by Y. Peng and C. Zhao (2012) and extend a result of J. Talbot (2002). We also establish an upper bound of the clique number in terms of Lagrangians for hypergraphs.

• Proceedings of the Korea Information Processing Society Conference
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• 2022.05a
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• pp.9-11
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• 2022

Community detection is a hot topic in social network analysis, and many existing studies use graph theory analysis methods to detect communities. This paper focuses on detecting absolute fair maximal balanced cliques in signed attributed social networks, which can satisfy ensuring the fairness of complex networks and break the bottleneck of the "information cocoon".

• Korean Management Science Review
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• v.12 no.2
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• pp.31-42
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• 1995

The ordering method is used to reduce the fill-ins in interior point methods. In ordering, the data structure plays an important role. In this paper, first, we compare the efficiency and the memory storage requirement of the quotient graph structure and the clique storage. Next, we propose a method of reducing the number of cliques and a data structure for clique storage. Finally, we apply a method of merging rows and absorbing cliques and show the experimental results.

• Electronics and Telecommunications Trends
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• v.8 no.4
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• pp.177-185
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• 1993

본 고에서는 기존의 maximal cliques 탐색 알고리즘들을 조사하여 분석하고 문제점들을 제시하여 상호 비교 분석함으로써 maximal cliques를 탐색하는 분야에 대한 알고리즘의 체계를 파악하고 기여할 수 있도록 노력하였다. 특히 기존의 clique 탐색 알고리즘들을 그들이 사용하는 기법에 따라서 point sequence method, line addition and removal technique, backtracking technique, 그리고 stack operation technique로 분류하고 각 기법에 해당하는 사례 알고리즘들을 분석하여 장단점들을 파악하며 상호 비교 분석하는데 그 초점을 맞추었다.

• Journal of the Korea Society of Computer and Information
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• v.20 no.1
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• pp.227-235
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• 2015

In this paper, I propose a linear time algorithm devised to produce exact solution to NP-complete maximum clique problem. The proposed algorithm firstly, from a given graph G=(V,E), sets vertex $v_i$ of the maximum degree ${\Delta}(G)$ as clique's major vertex. It then selects vertex $v_j$ of ${\Delta}(G)$ among vertices $N_G(v_i)$ that are adjacent to $v_i$, only to determine $N_G(v_i){\cap}N_G(v_j)$ as candidate cliques w and $v_k$. Next it obtains $w=w{\cap}N_G(v_k)$ by sorting $d_G(v_k)$ in the descending order. Lastly, the algorithm executes the same procedure on $G{\backslash}w$ graph to compare newly attained cliques to previously attained cliques so as to choose the lower. With this simple method, multiple independent cliques would also be attainable. When applied to various regular and irregular graphs, the algorithm proposed in this paper has obtained exact solutions to all the given graphs linear time O(n).

• Journal of Information Processing Systems
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• v.20 no.2
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• pp.200-214
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• 2024

Amid the flood of data, social network analysis is beneficial in searching for its hidden context and verifying several pieces of information. This can be used for detecting the spread model of infectious diseases, methods of preventing infectious diseases, mining of small groups and so forth. In addition, community detection is the most studied topic in social network analysis using graph analysis methods. The objective of this study is to examine signed attributed social networks and identify the maximal balanced cliques that are both absolute and fair. In the same vein, the purpose is to ensure fairness in complex networks, overcome the "information cocoon" bottleneck, and reduce the occurrence of "group polarization" in social networks. Meanwhile, an empirical study is presented in the experimental section, which uses the personal information of 77 employees of a research company and the trust relationships at the professional level between employees to mine some small groups with the possibility of "group polarization." Finally, the study provides suggestions for managers of the company to align and group new work teams in an organization.

• Korean Journal of Radiology
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• v.24 no.10
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• pp.933-935
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• 2023

• Management Science and Financial Engineering
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• v.8 no.1
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• pp.1-19
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• 2002

Ordering is used to reduce the amount of fill-ins in the Cholesky factor of a symmetric positive definite matrix. One of the most efficient ordering methods is the minimum degree ordering algorithm(MDO). In this paper, we provide a few techniques that improve the performance of MDO implemented with the clique storage scheme. First, the absorption of nodes in the cliques is developed which reduces the number of cliques and the amount of storage space required for MDO. Second, we present a modified minimum degree ordering algorithm of which the number of degree updates can be reduced by introducing the lower bounds of degrees. Third, using both the lower and upper bounds of degrees, we develop an approximate minimum degree ordering algorithm. Experimental results show that the proposed algorithm is competitive with the minimum degree ordering algorithm that uses quotient graphs from the points of the ordering time and the nonzeros in the Cholesky factor.