• 대한수학회논문집
• /
• 제18권4호
• /
• pp.745-754
• /
• 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.

• 대한수학회보
• /
• 제52권5호
• /
• pp.1423-1431
• /
• 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.

• 한국정보과학회:학술대회논문집
• /
• 한국정보과학회 2001년도 봄 학술발표논문집 Vol.28 No.1 (B)
• /
• pp.124-126
• /
• 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
• /
• 제19권2호
• /
• pp.189-202
• /
• 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
• /
• 제11권1호
• /
• pp.65-70
• /
• 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.

• 전자통신동향분석
• /
• 제8권4호
• /
• pp.177-185
• /
• 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.

• 대한산업공학회지
• /
• 제24권3호
• /
• pp.407-416
• /
• 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
• /
• 제28권3호
• /
• pp.405-419
• /
• 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.

• 전자공학회논문지A
• /
• 제31A권1호
• /
• pp.84-92
• /
• 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.

• 정보처리학회논문지B
• /
• 제10B권7호
• /
• pp.769-776
• /
• 2003

MCP(Maximal Clique Problem)를 해결하기 위해 DNA 컴퓨팅이 사용되고 있다. 그러나 현재의 DNA 컴퓨팅을 MCP에 적용하였을 때, 정점과 간선을 효율적으로 표현할 수 없으며 제한 효소의 잘못된 사용으로 인하여 해를 찾을 수 없는 문제점을 가지고 있다. 본 논문에서는 MCP의 문제점을 해결하기 위해 DNA 컴퓨팅 기법에 DNA 코딩 방법을 적용한 ACO(Algorithm for Code Optimization)를 제안한다. 우리는 ACO를 MCP에 적용하였고, 그 결과 ACO는 Adleman의 DNA 컴퓨팅 알고리즘 보다 가변길이의 DNA 코드를 표현할 수 있으며, 불필요한 정점을 제거한 코드를 생성할 수 있었다. 또한 ACO는 Adleman의 DNA 컴퓨팅 알고리즘 보다 탐색 시간과 생물학적 오류율을 15% 정도 줄임으로써 4배 정도 많은 최종해를 얻을 수 있었다.