• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.745-754
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• 2003

Maximum clique problem is to find a maximum clique(largest in size) in an undirected graph G. We present a method that computes either a maximum clique or an upper bound for the size of a maximum clique in G. We show that this method performs well on certain class of graphs and discuss the application of this method in a branch and bound algorithm for solving maximum clique problem, whose efficiency is depended on the computation of good upper bounds.

• 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.

• Proceedings of the Korean Information Science Society Conference
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• 2001.04b
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• pp.124-126
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• 2001

최근 데이터마이닝 응용분야에서 대용량의 고차원 데이터가 증가하고 있기 때문에 이를 효율적으로 처리할 수 있는 방법이 요구된다. 이를 위해 CLIQUE 방법과 셀-기반 클러스터링 방법을 선택하기 위해, 셀-기반 클러스터링 방법을 CLIQUE 방법 및 CLIQUE 방법에 근사정보(Approximation)를 결합한 방법과 성능 비교를 수행한다. 성능비교 결과, 셀-기반 클러스터링 방법이 데이터 클러스터링 및 데이터 검색시간에서 가장 우수한 성능을 보이며, 정확율은 CLIQUE 방법에 비해 다소 뒤떨어지거나 전체적인 효율성에서 매우 우수한 성능을 보인다.

• Journal of Information Processing Systems
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• v.19 no.2
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• pp.189-202
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• 2023

In the era marked by information inundation, social network analysis is the most important part of big data analysis, with clique detection being a key technology in social network mining. Also, detecting maximal balance clique in signed networks with positive and negative relationships is essential. In this paper, we present two algorithms. The first one is an algorithm, MCDA1, that detects the maximal balance clique using the improved three-way concept lattice algorithm and object-induced three-way concept lattice (OE-concept). The second one is an improved formal concept analysis algorithm, MCDA2, that improves the efficiency of memory. Additionally, we tested the execution time of our proposed method with four real-world datasets.

• Korean Journal of Mathematics
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• v.11 no.1
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• pp.65-70
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• 2003

We show that every quasi-random graph $G(n)$ with $n$ vertices and minimum degree $(1+o(1))n/2$ has diameter either 2 or 3 and that every quasi-random graph $G(n)$ with n vertices has a clique number of $o(n)$ with wide spread.

• 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 Korean Institute of Industrial Engineers
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• v.24 no.3
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• pp.407-416
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• 1998

For fast Cholesky factorization, it is most important to reduce the number of nonzero elements by ordering methods. Generally, the minimum deficiency ordering produces less nonzero elements, but it is very slow. We propose an efficient implementation method. The minimum deficiency ordering requires much computations related to adjacent nodes. But, we reduce those computations by using indistinguishable nodes, the clique storage structures, and the explicit storage structures to compute deficiencies.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.405-419
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• 2020

The zeroth-order general Randić index ⁰R_α(G) of the graph G is defined as ∑_u∈V(G)d(u)^α, where d(u) is the degree of vertex u and α is an arbitrary real number. In this paper, the maximum value of zeroth-order general Randić index on the graphs of order n with a given clique number is presented for any α ≠ 0, 1 and α ∉ (2, 2n-1], where n = |V (G)|. The minimum value of zeroth-order general Randić index on the graphs with a given clique number is also obtained for any α ≠ 0, 1. Furthermore, the corresponding extremal graphs are characterized.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.1
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• pp.84-92
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• 1994

In this paper, we present a novel scheduling algorithm using the weighted interval graph. An interval graph is constructed, where an interval is a time frame of each operation. And for each operation type, we look for the maximum clique of the interval graph: the number of nodes of the maximum clique represents the number of operation that are executed concurrently. In order to minimize resource cost. we select the operation type to reduce the number of nodes of a maximum clique. For the selected operation type, an operation selected by selection rule is moved to decrease the number of nodes of a maximum clique. A selected operation among unscheduled operations is moved repeatly and assigned to a control step consequently. The proposed algorithm is applied to the pipeline and the nonpipeline data path synthesis. The experiment for examples shows the efficiency of the proposed scheduling algorithm.

• The KIPS Transactions:PartB
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• v.10B no.7
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• pp.769-776
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• 2003

DNA computing has used to solve MCP (Maximal Clique Problem). However, when current DNA computing is applied to MCP. it can't efficiently express vertices and edges and it has a problem that can't look for solutions, by misusing wrong restriction enzyme. In this paper we proposed ACO (Algorithm for Code Optimization) that applies DNA coding method to DNA computing to solve MCP's problem. We applied ACO to MCP and as a result ACO could express DNA codes of variable lengths and generate codes without unnecessary vertices than Adleman's DNA computing algorithm could. In addition, compared to Adleman's DNA computing algorithm, ACO could get about four times as many as Adleman's final solutions by reducing search time and biological error rate by 15%.