• Honam Mathematical Journal
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• v.25 no.1
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• pp.95-115
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• 2003

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p{\geq}4)$ under the quadratic loss, based on a sample $X_1,\;{\cdots}X_n$. We find an optimal decision rule within the class of Lindley type decision rules which shrink the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm $||{\theta}-{\bar{\theta}}1||$ is known, where ${\bar{\theta}}=(1/p)\sum_{i=1}^p{\theta}_i$ and 1 is the column vector of ones. When the norm is restricted to a known interval, typically no optimal Lindley type rule exists but we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1027-1039
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• 2005

Consider the problem of estimating a $p{\times}1$ mean vector $\theta(p\geq4)$ under the quadratic loss, based on a sample $X_1$, $X_2$, $\cdots$, $X_n$. We find a Lindley type decision rule which shrinks the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm $\parallel\;{\theta}-\bar{{\theta}}1\;{\parallel}$ is restricted to a known interval, where $bar{{\theta}}=\frac{1}{p}\;\sum\limits_{i=1}^{p}{\theta}_i$ and 1 is the column vector of ones. In this case, we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.36C no.10
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• pp.66-74
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• 1999

In this paper, we propose a generalized model of statistical Hopfield neural network applicable to solving the well known NP-Complete problem, TSP. Van Den Bout's method to simplify the energy function through normalization has severe weak points that it does not consider the necessary perturbation effects. In proposed model, the improved energy function is used and 5 kinds of perturbation effects and the ratio between perturbation effects are considered including van Den Bout's 2 kinds and one more kind of Park. Through the simulation of randomly generated distribution of 10-city, it is found that our model shows 90 out of 100 cases reach the optimum and near optimum solution(within 5% error). We show the simulation of the large scale, 30-city and 50-city.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.11 no.6
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• pp.193-205
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• 2011

This paper suggests $p$-facility locations in $m$ candidate locations and $n$ areas in optimal cost side(population${\times}$shortest distance). This problem has been classified by NP-complete because there is not a polynomial time algorithm. In this paper, we suggests reverse-delete method that deletes a candidate facility one by one from $p=m$ until $p=2$. As a result of the proposed algorithm for the $5{\times}5$ and $7{\times}7$, the initial solution is obtained. For the Swain's 55-node network, we obtain the optimal solution through a solution improvement process with $p=4$ and it by using the initial solution with $p=5$.

• 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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.1
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• pp.157-162
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• 2023

To NP-complete 3-SAT problem, this paper proposes a O(nm) polynomial time algorithm, where n is the number of literals and m is the total frequency of all literals in equation f. The algorithm firstly decides a truth value of a literal in sequence of previously-set priority. The priority order is as follows: a literal whose occurrence in a clause is 1(k=1), a literal which is k≥2 and whose truth value is either 0 or 1, and a literal with the minimum frequency. Then, literals whose truth value is determined are then deleted from clause T and the remaining clauses. This process is repeated l times, the number of literals. As a result, the proposed algorithm has been successful in accurately determining the satisfiability of a given equation f and in deciding the truth value of all the literals. This paper, therefore, provides not only a linear-time algorithm as a viable solution to the SAT problem, but also a basis for solving the P versus NP problem.

• Journal of Integrative Natural Science
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• v.11 no.3
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• pp.154-160
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• 2018

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p-r{\geq}3)$, r = rank(K) with a projection matrix K under the quadratic loss, based on a sample $Y_1$, $Y_2$, ${\cdots}$, $Y_n$. In this paper a James-Stein type estimator with shrinkage form is given when it's variance distribution is specified and when the norm ${\parallel}{\theta}-K{\theta}{\parallel}$ is constrain, where K is an idempotent and symmetric matrix and rank(K) = r. It is characterized a minimal complete class of James-Stein type estimators in this case. And the subclass of James-Stein type estimators that dominate the sample mean is derived.

• 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.21 no.3
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• pp.1-8
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• 2016

The printed circuit board (PCB) can be used only 2 layers of front and back. Therefore, the wiring line segments are located in 2 layers without crossing each other. In this case, the line segment can be appear in both layers and this line segment is to resolve the crossing problem go through the via. The via minimization problem (VMP) has minimum number of via in layout design problem. The VMP is classified by NP-complete because of the polynomial time algorithm to solve the optimal solution has been unknown yet. This paper suggests polynomial time algorithm that can be solve the optimal solution of VMP. This algorithm transforms n-line segments into vertices, and p-crossing into edges of a graph. Then this graph is partitioned into 3-coloring sets of each vertex in each set independent each other. For 3-coloring sets $C_i$, (i=1,2,3), the $C_1$ is assigned to front F, $C_2$ is back B, and $C_3$ is B-F and connected with via. For the various experimental data, though this algorithm can be require O(np) polynomial time, we obtain the optimal solution for all of data.

• The Journal of Korean Academy of Prosthodontics
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• v.45 no.3
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• pp.295-302
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• 2007

Statement of problem. Fracture of the tooth-colored superstructure material is one of the main prosthetic complications in implant-supported prostheses. Purpose. The purpose of this in vitro study was to compare the fracture strength between the cement-retained implant-supported metal-ceramic crowns and the indirect composite resinveneered metal crowns under the vertical compressive load. Material and methods. Standard implants of external type (AVANA IFR 415 Pre-mount; Osstem Co., Busan, Korea) were embedded in stainless steel blocks perpendicular to their long axis. Customized abutments were fabricated using plastic UCLA abutments (Esthetic plastic cylinder; Osstem Co., Busan, Korea). Thirty standardized copings were cast with non-precious metal (Rexillium III, Pentron, Walling ford, Conn., USA). Copings were divided into two groups of 15 specimens each (n = 15). For Group I specimens, metal-ceramic crowns were fabricated. For Group II specimens, composite resin-veneered (Sinfony, 3M-ESPE, St. Paul, MN, USA) metal crowns (Sinfony-veneered crowns) were fabricated according to manufacturer's instructions. All crowns were temporary cemented and vertically loaded with an Instron universal testing machine (Instron 3366, Instron Corp., Norwood, MA, USA). The maximum load value (N) at the moment of complete failure was recorded and all data were statistically analyzed by independent sample t-test at the significance level of 0.05. The modes of failure were also investigated with visual analysis. Results. The fracture strength of Sinfony-veneered crowns ($2292.7{\pm}576.0N$) was significantly greater than that of metal-ceramic crowns ($1150.6{\pm}268.2N$) (P < 0.05). With regard to the failure mode, Sinfony-veneered crowns exhibited adhesive failure, while metal-ceramic crowns tended to fracture in a manner that resulted in combined failure. Conclusion. Sinfony-veneered crowns demonstrated a significantly higher fracture strength than that of metal-ceramic crowns in cement-retained implant-supported prostheses.