• 한국컴퓨터정보학회논문지
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• 제20권1호
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• pp.227-235
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• 2015

본 논문은 NP-완전으로 알려진 최대 클릭의 정확한 해를 선형시간으로 찾는 알고리즘을 제안하였다. 먼저, 주어진 그래프 G=(V,E)에서 최대 차수 ${\Delta}(G)$ 정점 $v_i$를 클릭의 대표 정점으로 결정한다. $v_i$ 인접 정점 $N_G(v_i)$에서 ${\Delta}(G)$ 정점 $v_j$를 선택하여 $N_G(v_i){\cap}N_G(v_j)$를 후보 클릭 w와 $v_k$로 결정한다. $d_G(v_k)$ 내림차순으로 $w=w{\cap}N_G(v_k)$를 얻는다. 마지막으로, $G{\backslash}w$그래프에서 동일한 절차를 수행하여 얻은 클릭이 기존에 얻은 클릭과 동일하거나 크면 이 클릭을 선정하는 검증과정을 거쳤다. 이와 같은 방법으로 독립된 다수의 클릭도 얻을 수 있는 장점이 있다. 제안된 알고리즘을 다양한 정규와 비정규 그래프에 적용한 결과 모든 그래프에 대해 선형시간 O(n)으로 정확한 해를 구하였다.

• 대한수학회보
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• 제54권3호
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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.

• 대한산업공학회지
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• 제29권1호
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• pp.78-89
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• 2003

Ordering is performed to reduce the amount of fill-ins of the Cholesky factor of a symmetric positive definite matrix. This paper proposes a new ordering algorithm that reduces the fill-ins of the Cholesky factor iteratively by elimination tree rotations and clique separators. Elimination tree rotations have been used mainly to reorder the rows of the permuted matrix for the efficiency of storage space management or parallel processing, etc. In the proposed algorithm, however, they are repeatedly performed to reduce the fill-ins of the Cholesky factor. In addition, we presents a simple method for finding a minimal node separator between arbitrary two nodes of a chordal graph. The proposed reordering procedure using clique separators enables us to obtain another order of rows of which the number of till-ins decreases strictly.

• Journal of Information Processing Systems
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• 제15권5호
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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.

• 대한수학회보
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• 제56권3호
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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.

• Journal of the Korean Data and Information Science Society
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• 제27권5호
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• pp.1273-1284
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• 2016

본 연구에서는 기계 학습 분야의 특허를 수집하여 키워드 네트워크를 구축하고 클릭 분석을 실시하였다. 먼저 텍스트 마이닝 기법을 적용하여 핵심 키워드들을 선정한 다음, 이 키워드를 기반으로 키워드 네트워크를 구축하였다. 다음으로 네트워크 구조 분석, 중요 키워드 분석 및 클릭 분석을 시행하여 2005년도와 2015년도에 출원된 기계 학습 특허의 동향을 파악하였을 뿐만 아니라 양해년도의 분석 결과를 통해 특허 경향을 파악하였다. 분석 결과 기계 학습 특허의 키워드 네트워크는 밀도와 군집 계수가 낮은 것으로 드러났으며 기계 학습 기법 자체에 대한 특허보다는 다양한 응용 영역에서 기계학습을 적용한 특허들이 다수이기 때문으로 판단된다. 클릭 분석 결과 2005년도 클릭 분석에 의해 발견된 주제는 뉴스메이커 검증, 상품 소비 예측, 바이러스 공격 예방, 바이오마커, 그리고 워크플로우 관리였으며, 2015년도 기계 학습 특허 주제는 디지털 이미지 편집, 직불카드, 수신자 인라이닝 시스템, 유방 촬영 시스템, 재고 관리 시스템, 이미지 편집 시스템, 비행기 티켓 가격 예측, 그리고 문제 예측 시스템으로 나타났다. 2005년도에 비하여 2015년도의 근접 중앙성은 낮아지고 매개 중심성은 높아진 것으로 보아 최근의 특허 경향은 보다 다양한 분야에서 출원되고 있으며 이들 간의 연결이 활발해지고 있음을 알 수 있다. 클릭 분석은 클릭을 형성하는 키워드 집합을 해석하여 주제를 파악하는데 활용될 수 있을 뿐만 아니라 추출된 공유 멤버쉽 키워드 집합은 특허 검색 시스템과 같이 키워드 검색 기반의 시스템에서 검색 키워드로 활용될 수 있을 것으로 기대된다.

• 경영과학
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• 제12권2호
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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.

• 한국생물정보학회:학술대회논문집
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• 한국생물정보시스템생물학회 2005년도 BIOINFO 2005
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• pp.228-233
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• 2005

The protein side-chain packing problem (SCPP) is known to be NP-complete. Various graph theoretic based side-chain packing algorithms have been proposed. However as the size of the protein becomes larger, the sampling space increases exponentially. Hence, one approach to cope with the time complexity is to decompose the graph of the protein into smaller subgraphs. Some existing approaches decompose the graph into biconnected components at an articulation point (resulting in an at-most 21-residue subgraph) or solve the SCPP by tree decomposition (4-, 5-residue subgraph). In this regard, we had also presented a deterministic based approach called as SPWCQ using the notion of maximum edge weight clique in which we reduce SCPP to a graph and then obtain the maximum edge-weight clique of the obtained graph. This algorithm performs well for a protein of less than 500 residues. However, it fails to produce a feasible solution for larger proteins because of the size of the search space. In this paper, we present a new heuristic approach for the side-chain packing problem based on the maximum edge-weight clique finding algorithm that enables us to compute the side-chain packing of much larger proteins. Our new approach can compute side-chain packing of a protein of 874 residues with an RMSD of 1.423${\AA}$.

• 대한수학회지
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• 제54권3호
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• pp.847-865
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• 2017

For a finite or an infinite set X, let $2^X$ be the power set of X. A class of simple graph, called strong Boolean graph, is defined on the vertex set $2^X{\setminus}\{X,{\emptyset}\}$, with M adjacent to N if $M{\cap}N={\emptyset}$. In this paper, we characterize the annihilating-ideal graphs $\mathbb{AG}(R)$ that are blow-ups of strong Boolean graphs, complemented graphs and preatomic graphs respectively. In particular, for a commutative ring R such that AG(R) has a maximum clique S with $3{\leq}{\mid}V(S){\mid}{\leq}{\infty}$, we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a complemented graph, if and only if R is a reduced ring. If assume further that R is decomposable, then we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a blow-up of a pre-atomic graph. We also study the clique number and chromatic number of the graph $\mathbb{AG}(R)$.

• Journal of Information Processing Systems
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• 제16권2호
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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.