• 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 KIISE:Software and Applications
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• v.36 no.11
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• pp.875-890
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• 2009

Metabolimics interprets an organism as a network of functional units and an organism is represented by a metabolic pathway i.e., well-displayed graph. So a software tool for drawing pathway is necessary to understand it comprehensively. These tools have a problem that edge-crossings exponentially increase as the number of nodes grows. To apply automatic graph layout techniques to the genome-scale metabolic flow, it is very important to reduce unnecessary edge-crossing on a metabolic pathway layout. In this paper, we design and implement 2.5D metabolic pathway layout modules. Metabolic pathways are represented hierarchically by making use of the '2-layered layout algorithm' in 3D. It enhances the readability and reduces unnecessary edge-crossings by using 3D layout modules instead of 2D layout algorithms.

• The KIPS Transactions:PartD
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• v.10D no.2
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• pp.261-266
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• 2003

A protein, which is a linear polymer of amino acids, is one of the most important bio-molecules composing biological structures and regulating bio-chemical reactions. Since the characteristics and functions of proteins are determined by their amino acid sequences in principle, protein sequence determination is the starting point of protein function study. This paper proposes a protein sequence prediction method based on data mining techniques, which can overcome the limitation of previous bio-chemical sequencing methods. After applying multiple proteases to acquire overlapped protein fragments, we can identify candidate fragment sequences by comparing fragment mass values with peptide databases. We propose a method to construct multi-partite graph and search maximal paths to determine the protein sequence by assembling proper candidate sequences. In addition, experimental results based on the SWISS-PROT database showing the validity of the proposed method is presented.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.4
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• pp.1712-1731
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• 2016

In this paper, we propose a novel saliency detection framework via multiple random walks (MRW) which simulate multiple agents on a graph simultaneously. In the MRW system, two agents, which represent the seeds of background and foreground, traverse the graph according to a transition matrix, and interact with each other to achieve a state of equilibrium. The proposed algorithm is divided into three steps. First, an initial segmentation is performed to partition an input image into homogeneous regions (i.e., superpixels) for saliency computation. Based on the regions of image, we construct a graph that the nodes correspond to the superpixels in the image, and the edges between neighboring nodes represent the similarities of the corresponding superpixels. Second, to generate the seeds of background, we first filter out one of the four boundaries that most unlikely belong to the background. The superpixels on each of the three remaining sides of the image will be labeled as the seeds of background. To generate the seeds of foreground, we utilize the center prior that foreground objects tend to appear near the image center. In last step, the seeds of foreground and background are treated as two different agents in multiple random walkers to complete the process of salient object detection. Experimental results on three benchmark databases demonstrate the proposed method performs well when it against the state-of-the-art methods in terms of accuracy and robustness.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.5_6
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• pp.176-186
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• 2007

An interconnection network can be represented as a graph where a vertex corresponds to a node and an edge corresponds to a link. The diameter of an interconnection network is the maximum length of the shortest paths between all pairs of vertices. The fault diameter of an interconnection network G is the maximum length of the shortest paths between all two fault-free vertices when there are $_k(G)-1$ or less faulty vertices, where $_k(G)$ is the connectivity of G. The fault diameter of an R-regular graph G with diameter of 3 or more and connectivity ${\tau}$ is at least diam(G)+1 where diam(G) is the diameter of G. We show that the fault diameter of a 2-dimensional $m{\times}n$ torus with $m,n{\geq}3$ is max(m,n) if m=3 or n=3; otherwise, the fault diameter is equal to its diameter plus 1. We also show that in $d({\geq}3)$-dimensional $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ torus with each $k_i{\geq}3$, there are 2d mutually disjoint paths joining any two vertices such that the lengths of all these paths are at most diameter+1. The paths joining two vertices u and v are called to be mutually disjoint if the common vertices on these paths are u and v. Using these mutually disjoint paths, we show that the fault diameter of $d({\geq}3)$-dimensional $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ totus with each $k_i{\geq}3$ is equal to its diameter plus 1.

• IEMEK Journal of Embedded Systems and Applications
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• v.7 no.2
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• pp.71-78
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• 2012

Based on the Zigbee-based wireless sensor network, I suggest the way to reduce errors between the short distance, improving the accuracy of the presumed distance by revising the deviation of RSSI(Received Signal Strength Indication) values is to estimate the distance using only the RF signal power without the additional hardware. In general, the graph measured by RSSI values shows the proximity values which are ideally reduced in proportion to the distance under the free outdoor space in which LOS(Line-Of-Sight) is guaranteed. However, if the result of the received RSSI values are each substituted to the formula, it can produce a larger margin of error and less accurate measurement since it is based upon the premise that this free space is not affected by reflected waves or obstacles caused by the ground and electronic jamming engendered by the environment. Therefore, the purpose of this study is to reduce the margin of errors between the distances and to measure the proximity values with the ideal type of graph by suggesting the way to revise the received RSSI values in the light of these reflected waves or obstacles and the electronic jamming. In conclusion, this study proves that errors are reduced by comparing the proposed deviation correction method to the revised RSSI value.

• Communications of Mathematical Education
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• v.21 no.2 s.30
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• pp.283-302
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• 2007

It is said that the university mathematics education in Korea faces critical situations due to the decreases of both qualities and quantities of students. In this paper we examine college students in order to know their basic ability for understanding about fundamental functions, such as polynomial, trigonometric, logarithm and exponential functions which have learned from highschool mathematics courses. The subject are 354 freshmen of 4 universities located in Daejeon and Chongchung area. The result of this study shows as follows. i ) More than half students are not able to draw graphs of given functions, except polynomial. ii ) More students do not fully understand about function properties such as domain, codomain, range, max and min value, cycle and parallel translation.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.211-222
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• 2017

In this paper, we consider three inverse eigenvalue problems for a special type of acyclic matrices. The acyclic matrices considered in this paper are described by a graph called a broom on n + m vertices, which is obtained by joining m pendant edges to one of the terminal vertices of a path on n vertices. The problems require the reconstruction of such a matrix from given partial eigen data. The eigen data for the first problem consists of the largest eigenvalue of each of the leading principal submatrices of the required matrix, while for the second problem it consists of an eigenvalue of each of its trailing principal submatrices. The third problem has an eigenvalue and a corresponding eigenvector of the required matrix as the eigen data. The method of solution involves the use of recurrence relations among the leading/trailing principal minors of ${\lambda}I-A$, where A is the required matrix. We derive the necessary and sufficient conditions for the solutions of these problems. The constructive nature of the proofs also provides the algorithms for computing the required entries of the matrix. We also provide some numerical examples to show the applicability of our results.

• International journal of advanced smart convergence
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• v.9 no.3
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• pp.192-198
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• 2020

The 3D point cloud is a key technology of object detection for virtual reality and augmented reality. In order to apply various areas of object detection, it is necessary to obtain 3D information and even color information more easily. In general, to generate a 3D point cloud, it is acquired using an expensive scanner device. However, 3D and characteristic information such as RGB and depth can be easily obtained in a mobile device. GNN (Graph Neural Network) can be used for object detection based on these characteristics. In this paper, we have generated RGB and RGBD by detecting basic information and characteristic information from the KITTI dataset, which is often used in 3D point cloud object detection. We have generated RGB-GNN with i-GNN, which is the most widely used LiDAR characteristic information, and color information characteristics that can be obtained from mobile devices. We compared and analyzed object detection accuracy using RGBD-GNN, which characterizes color and depth information.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.39-49
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• 2004

Let G be a simple graph and let $\={G}$ denotes its complement. We say that G is integral if its spectrum consists entirely of integers. If $\overline{aK_{a}\;{\bigcup}\;{\beta}K_{b}}$ is integral we show that it belongs to the class of integral graphs $[\frac{kt}{\tau}\;{x_0}\;+\;\frac{mt}{\tau}\;z}\;K_{(t+{\ell}n)+{\ell}m}\;\bigcup\;[\frac{kt}{\tau}\;{y_0}\;+\;\frac{(t\;+\;{\ell}n)k\;+\;{\ell}m}{\tau}\;z]n\;K_{em)$, where (i) t, k, $\ell$, m, $n\;\in\;\mathbb{N}$ such that (m, n) = 1, (n,t) = 1 and ($\ell,\;t$) = 1 ; (ii) $\tau\;=\;((t\;+\;{\ell}n)k\;+\;{\ell}m,\;mt)$ such that $\tau\;$\mid$kt$; (iii) ($x_0,\;y_0$) is a particular solution of the linear Diophantine equation $((t\;+\;{\ell}n)k\;+\;{\ell}m)x\;-\;(mt)y\;=\;\tau\;and\;(iv)\;z\;{\geq}\;{z_0}$ where $z_{0}$ is the least integer such that $(\frac{kt}{\tau}\;{x_0}\;+\;\frac{mt}{\tau}\;{z_0})\;\geq\;1\;and\;(\frac{kt}{\tau}\;{y_0}\;+\;\frac{(t+{\ell}n)k+{\ell}m}{\tau}\;{z_0})\;\geq\;1$.