• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.1
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• pp.128-133
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• 2022

This paper deals with the graph in which the weights of edges are given the distances between two end vertices on a metric space. In particular, we will study about a path P with n vertices for these graphs. We obtain a new graph $\bar{P}$ by augmenting an edge to P. Then the length of the shortest path between two vertices on $\bar{P}$ is considered and we focus on the maximum of these lengths. This maximum is called the diameter of the graph $\bar{P}$. We wish to find the augmented edge to minimize the diameter of $\bar{P}$. Especially, for an arbitrary real number λ > 0, we should determine whether the diameter of $\bar{P}$ is less than or equal to λ and we propose an O(n)-time algorithm for this problem, which improves on the time complexity O(nlogn) previously known. Using this decision algorithm, for the length D of P, we provide an O(nlogD)-time algorithm to find the minimum of the diameter of $\bar{P}$.

• Journal of the Korea Society of Computer and Information
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• v.23 no.12
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• pp.95-105
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• 2018

As the IT industry developed, the information held by the company soon became a corporate asset. As this information has value as an asset, the number and scale of various cyber attacks which targeting enterprises and institutions is increasing day by day. Therefore, research are being carried out to protect the assets from cyber attacks by using the attack graph to identify the possibility and risk of various attacks in advance and prepare countermeasures against the attacks. In the attack graph, security metric is used as a measure for determining the importance of each asset or the risk of an attack. This is a key element of the attack graph used as a criterion for determining which assets should be protected first or which attack path should be removed first. In this survey, we research trends of various security metrics used in attack graphs and classify the research according to application viewpoints, use of CVSS(Common Vulnerability Scoring System), and detail metrics. Furthermore, we discussed how to graft the latest security technologies, such as MTD(Moving Target Defense) or SDN(Software Defined Network), onto the attack graphs.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.603-612
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• 2021

We generalize 3-manifolds supporting non-positively curved metric to construct manifolds which have the following properties : (1) They are not locally CAT(0). (2) Their fundamental groups are residually finite. (3) They have subgroup separability for some abelian subgroups.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.255-271
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• 2023

In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.18 no.8
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• pp.2178-2198
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• 2024

Graph-based document models have good capabilities to reveal inter-dependencies among unstructured text data. Natural language processing (NLP) systems that use such models as an intermediate representation have shown good performance. This paper proposes a novel fuzzy graph-based document model and to demonstrate its effectiveness by applying fuzzy logic tools for text summarization. The proposed system accepts a text document as input and identifies some of its sentence level features, namely sentence position, sentence length, numerical data, thematic word, proper noun, title feature, upper case feature, and sentence similarity. The fuzzy membership value of each feature is computed from the sentences. We also propose a novel algorithm to construct the fuzzy graph as an intermediate representation of the input document. The Recall-Oriented Understudy for Gisting Evaluation (ROUGE) metric is used to evaluate the model. The evaluation based on different quality metrics was also performed to verify the effectiveness of the model. The ANOVA test confirms the hypothesis that the proposed model improves the summarizer performance by 10% when compared with the state-of-the-art summarizers employing alternate intermediate representations for the input text.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.209-224
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• 2024

The goal of this study is to instigate various new and novel optimum proximity point theorems using the notion of implicit relation type ℶ-proximal contraction for non-self mappings. An illustrated example is used to demonstrate the validity of the obtained results. Furthermore, some uniqueness results for proximal contractions are also furnished with partial order and graph. Various well-known discoveries in the present state-of-the-art are enhanced, extended, unified, and generalized by our findings. As an application, we generate some fixed point results fulfilling a modified contraction and a graph contraction, using the profundity of the established results.

• Journal of the Korea Computer Graphics Society
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• v.6 no.4
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• pp.23-28
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• 2000

We introduce a new method for constructing a dynamic Delaunay triangulation for a set S of n sites in the plane under the $L_{\infty}(L_1)$ metric. We find that the quadrant neighbor graph is contained in the Delaunay triangluation and that at least one edge of each triangle in the Delaunay triangulation is contained in the quadrant neighbor graph. By using these observations and employing a range tree scheme, we present a method that dynamically maintains the $L_{\infty}(L_1)$ Delaunay triangulation under insertions and deletions in $O(log^2n)$ amortized time and O(log n) expected time.

• Journal of Korea Multimedia Society
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• v.17 no.1
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• pp.34-42
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• 2014

In this paper an embedding algorithm based on commute time is implemented by organizing patches according to the graph-based metric, and its performance is analyzed by comparing with the results of principal component analysis embedding. It is usual that the dimensionality reduction be done within some acceptable approximation error. However this paper shows the proposed manifold embedding method generates the intrinsic geometry corresponding to the signal despite severe approximation error, so that it can be applied to the areas such as pattern classification or machine learning.

• Journal of KIISE:Computer Systems and Theory
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• v.28 no.3
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• pp.155-160
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• 2001

본 논문은 영역별 근접 그래프 (geographic nearest neighbor graph)와 레인지 트리 (range tree)를 이용하여 평면 위의 n 개의 점에 대한 L$_{\infty}$ (L$_1$) 거리 (metric) 상의 디루니 삼각분할 (Delaunay triangulation)을 구축하는 방법을 소개한다. 이 방법은 L$_{\infty}$ (L$_1$) 거리 상에서 디루니 삼각분할에 있는 각 삼각형의 최소한 한 선분이 영역별 근접 그래프에 포함됨을 이용하여 레인지 트리 방법으로 디루니 삼각분할을 구축한다. 본 방법은 0(nlogn)의 순차계산 시간에 L$_{\infty}$ (L$_1$) 디루니 삼각분할을 구축하며, CREW-PRAM (Concurrent Read Exclusive Write Parallel Random Access Machine)에서 0(n)의 프로세서로 0(logn)의 병렬처리 시간에 L$_{\infty}$ (L$_1$) 디루니 삼각분할을 구축한다. 또한, 이 방법은 직선간의 교차점 계산 대신 거리비교를 하기 때문에 수치오차가 적고 구현이 용이하다.

• Proceedings of the Korean Information Science Society Conference
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• 2000.10a
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• pp.545-547
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• 2000

본 논문은 영역별 근접 그래프(geographic nearest neighbor graph)와 레인지 트리(range tree)를 이용하여 평면 위의 n 개의 점에 대한 L$\infty$(L1) 거리(metric) 상의 디루니 삼각분할(Delaunay triangulation)을 구축하는 방법을 소개한다. 이 방법은 L$\infty$(L1) 거리상에서 디루니 삼각분할에 있는 각 삼각형의 최소한 한 선분이 영역별 근접 그래프에 포함됨을 이용하여 레인지 트리 방법으로 디루니 삼각분할을 구축한다. 본 방법은 O(nlogn)의 순차계산 시간에 L$\infty$(L1) 디루니 삼각분할을 구축하며, CREW-PRAM (Concurrent Read Exclusive Write Programmable Random Access Machine)에서 O(n)의 프로세서로 O(logn)의 병렬처리 시간에 L$\infty$(L1) 디루니 삼각분할을 구축한다. 또한, 이 방법은 직선간의 교차점 계산 대신 거리비교를 하기 때문에 수치오차가 적고 구현이 용이하다.