• 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 Institute of Information and Commucation Sciences Conference
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• 2007.06a
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• pp.470-473
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• 2007

Wireless Sensor Networks (WSNs) have merged to become one of the most promising applications of wireless ad hoc networks. A defer timer has been used in some of existing network protocols to solve a set of problems in WSNs. We first investigate the use of a defer timer to fully take the advantage of it in WSNs. We demonstrate that by properly setting up the defer timers, many difficult issues in sensor networks, such as power limitation, the broadcast storm problem, and the construction of the virtual backbone, can be easily tackled with only the help of simple localized information at each node. In this paper, we present the power of a defer timer in the design of dominating set construction protocol for broadcasting. The ns 2 computer simulations are carried out for performance study.

• 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 Korean Mathematical Society
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• v.46 no.6
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• pp.1309-1318
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• 2009

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A Roman k-dominating function on G is a function f : V (G) $\rightarrow$ {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices $\upsilon_1,\;\upsilon_2,\;{\ldots},\;\upsilon_k$ with $f(\upsilon_i)$ = 2 for i = 1, 2, $\ldot$, k. The weight of a Roman k-dominating function is the value f(V (G)) = $\sum_{u{\in}v(G)}$ f(u). The minimum weight of a Roman k-dominating function on a graph G is called the Roman k-domination number ${\gamma}_{kR}$(G) of G. Note that the Roman 1-domination number $\gamma_{1R}$(G) is the usual Roman domination number $\gamma_R$(G). In this paper, we investigate the properties of the Roman k-domination number. Some of our results extend these one given by Cockayne, Dreyer Jr., S. M. Hedetniemi, and S. T. Hedetniemi [2] in 2004 for the Roman domination number.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.12
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• pp.2865-2870
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• 2015

Recently, due to the hardware computing enhancement such as quantum computers, the amount of information that can be processed in a short period of time is growing exponentially. The cryptography system proposed by Koblitz and Fellows has a problem that it can not be guaranteed that the problem finding perfect dominating set is NP-complete in specific 3-regular graphs because the number of invariant polynomial can not be generated enough. In this paper, we propose an enhanced method to improve the vulnerability in 3-regular graph by generating plenty of invariant polynomials.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.279-287
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• 2015

A subset S of V (G), where G is a graph without isolated vertices, is a double dominating set of G if for each $x{{\in}}V(G)$, ${\mid}N_G[x]{\cap}S{\mid}{\geq}2$. This paper, shows that any positive integers a, b and n with $2{\leq}a<b$, $b{\geq}2a$ and $n{\geq}b+2a-2$, can be realized as domination number, double domination number and order, respectively. It also characterize the double dominating sets in the Cartesian and tensor products of two graphs and determine sharp bounds for the double domination numbers of these graphs. In particular, it show that if G and H are any connected non-trivial graphs of orders n and m respectively, then ${\gamma}_{{\times}2}(G{\square}H){\leq}min\{m{\gamma}_2(G),n{\gamma}_2(H)\}$, where ${\gamma}_2$, is the 2-domination parameter.

• Journal of Distribution Research
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• v.11 no.2
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• pp.97-122
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• 2006

A common assumption in marketing channel is that assortment benefits consumers. Recent research, however, has suggested that increasing the size of the choice set may have adverse consequences on the consumer choice. This research is to identify several factors that could affect the consumer choice in the context of product assortment. Especially, this research focus on the influence of the number of alternatives on the likelihood of purchase from the choice set. The preference for the no-choice option decreases as the number of alternatives increases. And it becomes higher when a dominating alternatives is present. And familiarity are considered as a factor affecting consumer's preference for a no-choice option. When a dominating alternatives is present, there is a positive and significant interaction between familarity and choice set size. It concludes with a discussion of the implications of the research findings and directions for future research.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.2
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• pp.128-133
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• 2010

This paper presents a method for estimating the parameters of dynamic models for induction motor dominating loads. Using particle swarm optimization, the method finds the adequate set of parameters that best fit the sampling data from the measurement for a period of time, minimizing the error of the outputs, active and reactive power demands and satisfying the steady-state error criterion.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.463-472
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• 2005

In this paper, the problem of estimating a p-variate (p $\ge$4) normal mean vector is considered in decision-theoretic set up. Using a simple property of the noncentral chi-square distribution, a sequence of estimators dominating the Lindley type estimator with the cases of unknown covariance matrices has been produced and each improved estimator is better than previous one.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1409-1418
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• 2021

In this paper, we study domination in the zero-divisor graph of a *-ring. We first determine the domination number, the total domination number, and the connected domination number for the zero-divisor graph of the product of two *-rings with componentwise involution. Then, we study domination in the zero-divisor graph of a Rickart *-ring and relate it with the clique of the zero-divisor graph of a Rickart *-ring.