• ETRI Journal
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• v.38 no.3
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• pp.540-550
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• 2016

Spectral clustering is a powerful tool for exploratory data analysis. Many existing spectral clustering algorithms typically measure the similarity by using a Gaussian kernel function or an undirected k-nearest neighbor (kNN) graph, which cannot reveal the real clusters when the data are not well separated. In this paper, to improve the spectral clustering, we consider a robust similarity measure based on the shared nearest neighbors in a directed kNN graph. We propose two novel algorithms for spectral clustering: one based on the number of shared nearest neighbors, and one based on their closeness. The proposed algorithms are able to explore the underlying similarity relationships between data points, and are robust to datasets that are not well separated. Moreover, the proposed algorithms have only one parameter, k. We evaluated the proposed algorithms using synthetic and real-world datasets. The experimental results demonstrate that the proposed algorithms not only achieve a good level of performance, they also outperform the traditional spectral clustering algorithms.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.749-756
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• 2003

네트워크에 속한 각 에지(edge)를 제거하는데 드는 비용 및 노드(node)들의 가중치가 주어져 있다고 가정하자. 네트워크 단절문제는 주어진 무방향 네트워크(undirected network)에 서 에지(edge)제거에 필요한 비용이 예산의 범위를 넘지 않도록 하면서, 원천노드(source node)와 연결이 끊어지는 노드들의 가중치의 합이 최대가 되도록 에지를 제거하는 방법을 찾는 문제이다. 이 문제는 Martel 등 [7]에 의해서 처음 소개되었고 NP hard임이 밝혀졌다. 또한 명영수와 김현준 [2]은 주어진 그래프의 특성을 이용하여 문제의 크기를 줄이는 과정과 수리계획모형을 제시하엿고, 제시된 모형을 이용하여 하한 및 상한을 도출하는 절차를 개발하였다. 본 연구에서는 문제의 특성을 주가로 규명하고 이를 이용하여 실행가능해를 도출하는 새로운 휴리스틱을 제시하며, 수리계획모형의 신형계획완화를 이용하여 상한을 도출할 때 유효부동식을 이용하여 개선된 상한을 구하는 방법을 제시하기로 한다. 아울러 충분한 계산실험을 통하여 개발된 해법의 성능을 평가하기로 한다.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.427-432
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• 1998

When an undirected tree T and a vertex ${\gamma}$ in the tree are given the problem to transform T into a rooted tree with ${\gamma}$ as its root is considered. Using Euler tour and prefix sum an optimal algorithm has been developed [2,3]. We will present another parallel algorithm which is optimal also on EREW PRAM. Our approach resuces the given tree step by step by pruning and pointer jumping. That is the tree structure is retained during algorithm processing such that than other tree computations can be carried out in parallel.

• The Mathematical Education
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• v.13 no.2
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• pp.6-10
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• 1974

We consider 'ordinary' graphs: that is, finite undirected graphs with no loops or multiple edges. An intersection representation of a graph G is a function r from V(G), the set of vertices of G, into a family of sets S such that distinct points $\chi$$_{\alpha}$ and $\chi$$_{\beta}$/ of V(G) are. neighbors in G precisely when ${\gamma}$($\chi$$_{\alpha}$)∩${\gamma}$($\chi$$_{\beta}$/)$\neq$ø, A graph G is a rigid circuit grouph if every cycle in G has at least one triangular chord in G. In this paper we consider the main theorem; A graph G has an intersection representation by arcs on an acyclic graph if and only if is a normal rigid circuit graph.uit graph.d circuit graph.uit graph.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.5
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• pp.434-441
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• 2015

In this paper, we propose an inverse optimal distributed protocol for the formation and velocity consensus of nonholonomic mobile robots. The communication among mobile robots is described by a simple undirected graph, and the mobile robots' kinematics are considered. The group of mobile robots driven by the proposed protocols asymptotically achieves the desired formation and group velocity in an inverse optimal fashion. The design of the protocols is based on dynamic feedback linearization and the proposed linear quadratic (LQ) inverse optimal second-order consensus protocol. A numerical simulation is given to verify the effectiveness of the proposed scheme.

• Korean Management Science Review
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• v.18 no.2
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• pp.107-116
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• 2001

In the ring leading problem with demand splitting, traffic demands are given for each pair of nodes in an undirected ring network and a flow is routed in either of the two directions, clockwise and counter-clockwise. The load of a link is the sum of the flows routed through the link and the objective of the problem is to minimize the maximum link load on the ring. Recently, four different optimal a1gorithms have been developed for solving the problem. In this paper, we compare those algorithms in a single framework and conduct a computational study to evaluate the practical performance of those algorithms.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.3
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• pp.49-62
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• 1998

In the ring loading problem, traffic demands are given for each pair of nodes in an undirected ring network with n nodes and a flow is routed in either of the two directions, clockwise and counter-clockwise. The load of a link is the sum of the flows routed through the link and the objective of the Problem is to minimize the maximum load on the ring. In the ring loading problem with integer demand splitting, each demand can be split between the two directions and the flow routed in each direction is restricted to integers. Recently, Vachani et al. ［INFORMS J. Computing 8 (1996) 235-242］ have developed an Ο(n$^3$) algorithm for solving this integer version of the ring loading problem and independently, Schrijver et al. ［to appear in SIAM J. Disc. Math.］ have presented an algorithm which solves the problem with ｛0,1｝ demands in Ο（n$^2$｜K｜ ) time where K denotes the index set of the origin-desㅇtination pairs of nodes having flow demands. In this paper, we develop an algorithm which solves the problem in Ο(n ｜K｜) time.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.569-578
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• 2020

Various graph clustering methods have been introduced to identify communities in social or biological networks. This paper studies the entropy-based and the Markov chain-based methods in clustering the undirected graph. We examine the performance of two clustering methods with conventional methods based on quality measures of clustering. For the real applications, we collect the mathematical subject classification (MSC) codes of research papers from published mathematical databases and construct the weighted code-to-document matrix for applying graph clustering methods. We pursue to group MSC codes into the same cluster if the corresponding MSC codes appear in many papers simultaneously. We compare the MSC clustering results based on the several assessment measures and conclude that the Markov chain-based method is suitable for clustering the MSC codes.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.3
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• pp.222-226
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• 2010

In this paper we study the consensus problem of SISO (Single-Input Single-Output) linear multi-agent systems under a fixed weighted undirected network communication. The dynamics of each agent can be of any order, while it is constrained to be neutrally stable. Based on a simple root locus argument, we show that the problem at hand is always solvable if the gain and zeros of the dynamic compensator, of which dimension is the same as the number of plant poles on the imaginary axis, are chosen suitably, finally the result is successfully verified by an example.

• The KIPS Transactions:PartB
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• v.15B no.6
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• pp.609-612
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• 2008

Let G = (V, E) be a simple undirected graph. The Minimum Vertex Cover (MVC) problem is to find a minimum subset C of V such that for every edge, at least one of its endpoints should be included in C. Like many other graph theoretic problems this problem is also known to be NP-hard. In this paper, we propose a genetic algorithm called LeafGA for MVC problem and show the performance of the proposed algorithm by applying it to several published benchmark graphs.