• The KIPS Transactions:PartA
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• v.18A no.2
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• pp.69-74
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• 2011

The minimum dominating set problem of a graph G is to find a smallest possible dominating set. The minimum dominating set problem is a well-known NP-complete problem such that it cannot be solved in polynomial time. Heuristic or approximation algorithm, however, will perform well in certain area of application. In this paper, we suggest three different simulated annealing algorithms and experimentally show better efficiency improvement by applying these algorithms to the graph instances developed by DIMACS.

• 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.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.

• 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 the Korean Operations Research and Management Science Society
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• v.39 no.2
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• pp.131-140
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• 2014

Customer networks go through constant changes. They may expand or shrink once they are formed. In dynamic environments, it is a critical corporate challenge to identify and manage influential customer groups in a cost effective way. In this context, we apply inverse optimization theory to suggest an efficient method to manage customer networks. In this paper, we assume that there exists a subset of nodes that might have a large effect on the network and that the network can be modified via some strategic actions. Rather than making efforts to find influential nodes whenever the network changes, we focus on a subset of selective nodes and perturb as little as possible the interaction between nodes in order to make the selected nodes influential in the given network. We define the following problem based on the inverse optimization. Given a graph and a prescribed node subset, the objective is to modify the structure of the given graph so that the fixed subset of nodes becomes a minimum dominating set in the modified graph and the cost for modification is minimum under a fixed norm. We call this problem the inverse dominating set problem and investigate its computational complexity.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.11 no.6
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• pp.183-191
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• 2011

This paper suggests emergency medical service vehicle (ambulance) algorithm when the emergency patient occurs in order to be sufficient the maximum permission time T of arrival about all sectors in one city that is divided in the various areas. This problem cannot be solved in polynomial times. One can obtains the solution using the integer programming. In this paper we suggest vertex set (or dominating set) algorithm and easily decide the location of ambulances. The core of the algorithm decides the location of ambulance is to the maximum degree vertex among the neighborhood of minimum degree vertex. For the 33 sectors Ostin city in Texas, we apply $3{\leq}T{\leq}20$ minutes. The traditional set cover algorithm with integer programming cannot obtains the solution in several T in 18 cases. But, this algorithm obtains solution for all of the 18 cases.