• 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).

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.1037-1067
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• 2017

Motzkin and Straus established a close connection between the maximum clique problem and a solution (namely graph-Lagrangian) to the maximum value of a class of homogeneous quadratic multilinear functions over the standard simplex of the Euclidean space in 1965. This connection and its extensions were successfully employed in optimization to provide heuristics for the maximum clique problem in graphs. It is useful in practice if similar results hold for hypergraphs. In this paper, we develop a homogeneous multilinear function based on the structure of hypergraphs and their complement hypergraphs. Its maximum value generalizes the graph-Lagrangian. Specifically, we establish a connection between the clique number and the generalized graph-Lagrangian of 3-uniform graphs, which supports the conjecture posed in this paper.

• 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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.273-273
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• 1996

• Journal of Information Processing Systems
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• v.15 no.5
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• pp.1141-1155
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• 2019

Today, most approaches used in the recommendation system provide correct data prediction similar to the data that users need. The method that researchers are paying attention and apply as a model in the recommendation system is the communities' detection in the big social network. The outputted result of this approach is effective in improving the exactness. Therefore, in this paper, the personalized movie recommendation system that combines data mining for the k-clique method is proposed as the best exactness data to the users. The proposed approach was compared with the existing approaches like k-clique, collaborative filtering, and collaborative filtering using k-nearest neighbor. The outputted result guarantees that the proposed method gives significant exactness data compared to the existing approach. In the experiment, the MovieLens data were used as practice and test data.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.359-370
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• 2020

A graph G is called a well covered graph if every maximal independent set in G is maximum, and co-well covered graph if its complement is a well covered graph. We study some properties of a co-well covered graph and we characterize when the join, the corona product, and cartesian product are co-well covered graphs. Also we characterize when powers of trees and cycles are co-well covered graphs. The line graph of a graph which is co-well covered is also studied.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.1
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• pp.269-276
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• 2015

This paper proves the Erd$\ddot{o}$s-Faber-Lov$\acute{a}$sz conjecture of the vertex coloring problem, which is so far unresolved. The Erd$\ddot{o}$s-Faber-Lov$\acute{a}$sz conjecture states that "the union of k copies of k-cliques intersecting in at most one vertex pairwise is k-chromatic." i.e., x(G)=k. In a bid to prove this conjecture, this paper employs a method in which it determines the number of intersecting vertices and that of cliques that intersect at one vertex so as to count a vertex of the minimum degree ${\delta}(G)$ in the Minimum Independent Set (MIS) if both the numbers are even and to count a vertex of the maximum degree ${\Delta}(G)$ in otherwise. As a result of this algorithm, the number of MIS obtained is x(G)=k. When applied to $K_k$-clique sum intersecting graphs wherein $3{\leq}k{\leq}8$, the proposed method has proved to be successful in obtaining x(G)=k in all of them. To conclude, the Erd$\ddot{o}$s-Faber-Lov$\acute{a}$sz conjecture implying that "the k-number of $K_k$-clique sum intersecting graph is k-chromatic" is proven.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1423-1431
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• 2015

A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number is the minimum cardinality of a clique-transversal set in G. For every cubic graph with at most two bridges, we first show that it has a perfect matching which contains exactly one edge of each triangle of it; by the result, we determine the exact value of the clique-transversal number of line graph of it. Also, we present a sharp upper bound on the clique-transversal number of line graph of a cubic graph. Furthermore, we prove that the clique-transversal number of line graph of a triangle-free graph is at most the chromatic number of complement of the triangle-free graph.

• Journal of Information Processing Systems
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• v.16 no.2
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• pp.494-507
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• 2020

This study proposed the movie recommendation system based on the user's personal information and movies rated using the method of k-clique and normalized discounted cumulative gain. The main idea is to solve the problem of cold-start and to increase the accuracy in the recommendation system further instead of using the basic technique that is commonly based on the behavior information of the users or based on the best-selling product. The personal information of the users and their relationship in the social network will divide into the various community with the help of the k-clique method. Later, the ranking measure method that is widely used in the searching engine will be used to check the top ranking movie and then recommend it to the new users. We strongly believe that this idea will prove to be significant and meaningful in predicting demand for new users. Ultimately, the result of the experiment in this paper serves as a guarantee that the proposed method offers substantial finding in raw data sets by increasing accuracy to 87.28% compared to the three most successful methods used in this experiment, and that it can solve the problem of cold-start.

• The Journal of the Korea Contents Association
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• v.10 no.6
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• pp.415-428
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• 2010

Converging technologies have become a major issue in science policy. This paper describes the current state of scientific collaboration for convergent technologies among researchers in South Korea, by conducting Social Network Analysis (SNA) with the data set of 1,095 researchers who have involved in the development of the convergent technologies. It is found that the researchers in convergent technology are more productive than the researchers in other technology domains. However, the researchers in convergent technologies have small number of collaborators, compared with their productivity. Only a few researchers have a role of the hub in the collaboration networks, meaning that the structure network is closer to than the core than the peripheral. The scientific collaboration network of the convergent technology researchers shows that the members of the network are close to each other, but there is small number of cliques.