• 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.

• 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.

• ETRI Journal
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• v.37 no.3
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• pp.480-490
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• 2015

The reliability of sensor networks is generally dependent on the battery power of the sensor nodes that it employs; hence it is crucial for the sensor nodes to efficiently use their battery resources. This research paper presents a method to increase the reliability of sensor nodes by constructing a connected dominating tree (CDT), which is a subnetwork of wireless sensor networks. It detects the minimum number of dominatees, dominators, forwarder sensor nodes, and aggregates, as well as transmitting data to the sink. A new medium access control (MAC) protocol, called Homogenous Quorum-Based Medium Access Control (HQMAC), is also introduced, which is an adaptive, homogenous, asynchronous quorum-based MAC protocol. In this protocol, certain sensor nodes belonging to a network will be allowed to tune their wake-up and sleep intervals, based on their own traffic load. A new quorum system, named BiQuorum, is used by HQMAC to provide a low duty cycle, low network sensibility, and a high number of rendezvous points when compared with other quorum systems such as grid and dygrid. Both the theoretical results and the simulation results proved that the proposed HQMAC (when applied to a CDT) facilitates low transmission latency, high delivery ratio, and low energy consumption, thus extending the lifetime of the network it serves.

• 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 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.

• 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.

• Proceedings of the Korean Information Science Society Conference
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• 2012.06d
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• pp.369-371
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• 2012

Wireless sensor networks have taken immense interest in healthcare systems in recent years. One example of it is in an in vivo sensor that is deployed in critical and sensitive healthcare applications like artificial retina, cardiac pacemaker, drug delivery, blood pressure, internal heat calculation, glucosemonitoring etc. In vivo sensor nodes exhibit temperature that may be very dangerous for human tissues. However, existing in vivo thermal aware routing approaches suffer from hotspot creation, delay, and computational complexity. These limitations motivate us toward an in vivo virtual backbone, a small subset of nodes, connected to all other nodes and involved in routing of all nodes, -based solution. A virtual backbone is lightweight and its fault-tolerant version allows in vivo sensor nodes to disconnect hotspot paths and to use alternative paths. We have formulated the problem as m-connected k-dominating set problem with minimum temperature cost in in vivo sensor network. This is a combinatorial optimization problem and we have been motivated to use evolutionary approach to solve the problem.

• Proceedings of the Korea Contents Association Conference
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• 2009.05a
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• pp.851-855
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• 2009

Constructing CDS in wireless ad-hoc network, it is necessary to make more efficient algorithm that is fast, simple and has low power consumption. It is worried about losing data which brought a bottleneck state from confliction and delay when the nodes are concentrated or CDS is reconstructed. So, after constructing most efficient CDS, It is better not to reconstruct CDS in moveless wireless ad-hoc network. In this paper, we compared and estimated the performance in each situation of a CDS construction algorithm based on Node degree and Energy level.

• Journal of the Korea Institute of Military Science and Technology
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• v.15 no.6
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• pp.770-778
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• 2012

In this paper, we propose a multi-path construction scheme to improve the survivability of a multicast session in military hybrid networks. A military hybrid network consists of a static backbone network and multiple mobile stub networks where some nodes are frequently susceptible to be disconnected due to link failure and node mobility. To improve the survivability of multicast sessions, we propose a construction scheme of ${\kappa}$ redundant multi-paths to each receiver. In order to take account of different characteristics of static and mobile networks, we propose quite different multi-path setup approaches for the backbone and stub networks, respectively, and combine them at the boundary point called gateway. We prove that our proposed scheme ensures that each receiver of a multicast session has ${\kappa}$ redundant paths to the common source. Through simulations, we evaluate the performance of the proposed schemes from three aspects : network survivability, recovery cost, and end-to-end delay.