• Journal of the Korea Society of Computer and Information
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• v.18 no.9
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• pp.121-129
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• 2013

This paper proposes a linear-time algorithm that has been designed to obtain an accurate solution for Dominating Set (DS) problem, which is known to be NP-complete due to the deficiency of polynomial-time algorithms that successfully derive an accurate solution to it. The proposed algorithm does so by repeatedly assigning vertex v with maximum degree ${\Delta}(G)$among vertices adjacent to the vertex v with minimum degree ${\delta}(G)$ to Minimum Independent DS (MIDS) as its element and removing all the incident edges until no edges remain in the graph. This algorithm finally transforms MIDS into Minimum DS (MDS) and again into Minimum Connected DS (MCDS) so as to obtain the accurate solution to all DS-related problems. When applied to ten different graphs, it has successfully obtained accurate solutions with linear time complexity O(n). It has therefore proven that Dominating Set problem is rather a P-problem.

• Journal of the Korea Society of Computer and Information
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• v.20 no.2
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• pp.63-70
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• 2015

In the absence of a polynomial time algorithm capable of obtaining the exact solutions to it, the domatic number problem (DNP) of dominating set (DS) has been regarded as NP-complete. This paper suggests polynomial-time complexity algorithm about DNP. In this paper, I select a vertex $v_i$ of the maximum degree ${\Delta}(G)$ as an element of a dominating set $D_i,i=1,2,{\cdots},k$, compute $D_{i+1}$ from a simplified graph of $V_{i+1}=V_i{\backslash}D_i$, and verify that $D_i$ is indeed a dominating set through $V{\backslash}D_i=N_G(D_i)$. When applied to 15 various graphs, the proposed algorithm has succeeded in bringing about exact solutions with polynomial-time complexity O(kn). Therefore, the proposed domatic number algorithm shows that the domatic number problem is in fact a P-problem.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.12
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• pp.2243-2251
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• 2016

In this paper, we propose a theoretical model for characterization and upper bounds of [1,2]-domination set of network which has tree structure. In detail, we propose a theoretic model for upper bounds on [1,2]-domination set of a tree network which has some typical constrains. To that purpose, we introduce a graph theory to model and analyze the characteristics of tree structure networks. We assume a node subset D of a graph G=(V,E). We define that D is a [1,2]-dominant set if for any node v in set V which is not an element of a set D is adjacent to a node or two nodes of an element in a set D (that is, $1{\leq}{\mid}N({\upsilon}){\bigcap}D{\mid}{\leq}2$ for every node $v{\in}V-D$). The minimum cardinality of a [1,2]-dominating set of G, which is denoted by ${\gamma}_{[1,2]}(G)$, is called the [1,2]-domination number of G. In this paper, we show new upper bounds and characteristics about the [1,2]-domination number of tree.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.4
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• pp.571-581
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• 2022

Wireless sensor networks use the concept of connected dominating sets that can form virtual backbones for effective routing and broadcasting. In this paper, we propose an optimization algorithm that configures a connected dominating sets in order to balance the load of nodes to increase network lifetime and to perform effective routing. The proposed optimization algorithm in this paper uses the metaheuristic method of tabu search algorithm, and is designed to balance the number of dominatees in each dominator in the constituted linked dominance set. By constructing load-balanced connected dominating sets with the proposed algorithm, it is possible to extend the network lifetime by balancing the load of the dominators. The performance of the proposed tabu search algorithm was evaluated the items related to load balancing on the wireless sensor network, and it was confirmed in the performance evaluation result that the performance was superior to the previously proposed method.

• Journal of the Korea Society of Computer and Information
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• v.16 no.6
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• pp.179-186
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• 2011

This paper suggests the minimum number of vertex guards algorithm. Given n rooms, the exact number of minimum vertex guards is proposed. However, only approximation algorithms are presented about the maximum number of vertex guards for polygon and orthogonal polygon without or with holes. Fisk suggests the maximum number of vertex guards for polygon with n vertices as follows. Firstly, you can triangulate with n-2 triangles. Secondly, 3-chromatic vertex coloring of every triangulation of a polygon. Thirdly, place guards at the vertices which have the minority color. This paper presents the minimum number of vertex guards using dominating set. Firstly, you can obtain the visibility graph which is connected all edges if two vertices can be visible each other. Secondly, you can obtain dominating set from visibility graph or visibility matrix. This algorithm applies various art galley problems. As a results, the proposed algorithm is simple and can be obtain the minimum number of vertex guards.

• Proceedings of the Korean Information Science Society Conference
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• 2010.06b
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• pp.493-496
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• 2010

본 논문은 평면 위의 점 집합에서 지배되지 않는 점 집합을 찾아내는 병렬 알고리즘을 제안한다. 우리는 먼저 기존의 지배되지 않는 점을 계산하는 문제가 SIMD형 병렬계산 장치인 GPU에서 병렬화가 가능하다는 사실을 보이고, 실제 GPU를 이용한 병렬 알고리즘을 설계 구현하였다. 또한 실험 결과 직렬 알고리즘에 비해 2배 이상의 성능 향상을 얻을 수 있었다.

• Proceedings of the Korean Information Science Society Conference
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• 2010.06a
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• pp.323-328
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• 2010

본 논문에서는 도로 네트워크에서 지배받지 않는(non-dominated) 점 집합을 찾는 문제를 다루었다. 지배받지 않는 자료는 다른 자료들에 비해 질의에 대해서 한 가지 조건이라도 우위에 있는 자료들을 의미한다. 본 논문에서 주어진 도로는 연결된 그래프의 형태로 주어지면 각 도로는 도로를 이용하는데 소요되는 시간을 가중치로 가진다. 우리는 지배성(dominance)과 지배받지 않는 자료의 성질을 이용하는 알고리즘을 우선 제시한다. 또한 이 방법이 지배받지 않는 점을 찾을 때 비효율적인 연산을 수행함을 보이고, 이 알고리즘과 시간복잡도는 동일하지만 비효율적인 부분을 개선하여 실제 수행시간이 향상된 알고리즘을 제시한다. 이와 함께 실험을 통해 개선된 수행성능을 보인다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.6
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• pp.1142-1147
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• 2015

As a method to increase the scalability and efficiency of wireless sensor networks, a scheme to construct networks hierarchically has received considerable attention among researchers. Researches on the methods to construct wireless networks hierarchically have been conducted focusing on how to select nodes such that they constitute a backbone network of wireless network. Nodes comprising the backbone network should be connected themselves and can cover other remaining nodes. A problem to find the minimum number of nodes which satisfy these conditions is known as the minimum connected dominating set (MCDS) problem. The MCDS problem is NP-hard, therefore there is no efficient algorithm which guarantee the optimal solutions for this problem at present. In this paper, we propose a novel multi-start local search algorithm to solve the MCDS problem efficiently. For the performance evaluation of the proposed method, we conduct extensive experiments and report the results.

• Journal of KIISE:Information Networking
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• v.34 no.3
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• pp.226-238
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• 2007

In this paper, we present a novel fully distributed topology control protocol that can construct the multiple-ring topology of Minimal Connected Dominating Set (MCDS) as the transport backbone for mobile ad hoc networks. It makes a topology from the minimal nodes that are chosen from all the nodes, and the constructed topology is comprised of the minimal physical links while preserving connectivity. This topology reduces the interference. The all nodes work as the nodes of the distributed parallel Boltzmann machine, of which the objective function is consisted of two Boltzmann factors: the link degree and the connection domination degree. To define these Boltzmann factors, we extend the Connected Dominating Set into a fuzzy set, and also define the fuzzy set of nodes by which the multiple-ring topology can be constructed. To construct the transport backbone of the mobile ad hoc network, the proposed protocol chooses the nodes that are the strong members of these two fuzzy sets as the clusterheads. We also ran simulations to provide the quantitative comparison against the related works in terms of the packet loss rate and the energy consumption rate. As a result, we show that the network that is constructed by the proposed protocol has far better than the other ones with respect to the packet loss rate and the energy consumption rate.

• Journal of the Korean School Mathematics Society
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• v.3 no.1
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• pp.211-217
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• 2000

본 논문의 목적은 G. Cantor 에 의하여 출발된 집합론을 보통집합 이론이라고 구별하여 부를 때, 보통 집합 이론이 그 바탕에 깔고 있는 논리적 제한 점들 곧, 배중률이라든지 모순의 법칙 등을 어떻게 보완할 수 있을 것인가\ulcorner 하는 점과 그러한 점을 보완하여야 할 필요성에 대하여도 생각하고자 한다. 그런 관점에서 보통집합 이론과 퍼지집합 이론의 기본개념을 상호 비교함으로써 앞서 제기한 문제의 보완 요소를 찾아보려고 한다. 실제에 있어 인간의 사고 가운데에서는 중간을 배제하는 일이 없음에도 불구하고 이를 수학적으로 접근하고 표현하는 수단이 부족함으로 인하여 부자연스러운 논리의 법칙을 받아들일 수밖에 없었던 것도 사실이다. 특히, 논리적 응용력이 부족한 중등과정의 학생들에게 있어서 수학이 전적으로 2가 논리에 의하여 지배되고 있다는 방식으로만 지도하는 것은 여러 가지 측면에서 그 내용의 보완이 요구된다. 보다 다양한 수학적 표현의 여지를 열어주는 지도법은 쉼없이 연구되어야 할 것이다. 무엇보다도 배우는 학생들이 보다 폭 넓은 사고의 영역을 소유하고, 그를 바탕으로 창의적이고 자유로운 발상이 이어 질 수 있도록 하기 위하여는 교사의 수학적 시야가 보다 넓고 유연해져야 한다함은 재론할 필요가 없을 것이다. 그런 의미에서 본 논문이 작은 역할을 할 수 있기를 바란다.