• The KIPS Transactions:PartA
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• v.9A no.2
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• pp.267-270
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• 2002

The evaluation of the cumulative distribution function of the noncentral $\chi^2$ distribution is required in approximate determination of the power of the $\chi^2$ test. This article provides an algorithm for evaluating the noncentral $\chi^2$ distribution function in terms of a single "central" $\chi^2$ distribution function and compared various approximations.ximations.

• The Journal of Korean Association of Computer Education
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• v.8 no.6
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• pp.103-111
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• 2005

This paper presents a novel automated threshold-decision algorithm that uses the mean and standard-deviation values obtained from the difference values of consecutive frames. At first, the calculation of difference values is obtained by the weighted ${\chi}^2$-test algorithm which was modified by joining color histogram to ${\chi}^2$-test algorithm. The weighted ${\chi}^2$-test algorithm can subdivide the difference values by imposing weights according to NTSC standard. In the first step, the proposed automatic threshold-decision algorithm calculates the mean and standard-deviation value from the total difference values, and then subtracts the mean value from the each difference values. In the next step, the same process is performed on the remained difference values, and lastly, the threshold is detected from the mean when the standard deviation has a maximum value. The proposed method is tested on various video sources and, in the experimental results, it is shown that the proposed method efficiently estimates the thresholds and reliably detects scene changes.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.5
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• pp.263-269
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• 2014

In this paper, I disprove Hadwiger conjecture of the vertex coloring problem, which asserts that "All $K_k$-minor free graphs can be colored with k-1 number of colors, i.e., ${\chi}(G)=k$ given $K_k$-minor." Pursuant to Hadwiger conjecture, one shall obtain an NP-complete k-minor to determine ${\chi}(G)=k$, and solve another NP-complete vertex coloring problem as a means to color vertices. In order to disprove Hadwiger conjecture in this paper, I propose an algorithm of linear time complexity O(V) that yields the exact solution to the vertex coloring problem. The proposed algorithm assigns vertex with the minimum degree to the Maximum Independent Set (MIS) and repeats this process on a simplified graph derived by deleting adjacent edges to the MIS vertex so as to finally obtain an MIS with a single color. Next, it repeats the process on a simplified graph derived by deleting edges of the MIS vertex to obtain an MIS whose number of vertex color corresponds to ${\chi}(G)=k$. Also presented in this paper using the proposed algorithm is an additional algorithm that searches solution of ${\chi}^{{\prime}{\prime}}(G)$, the total chromatic number, which also remains NP-complete. When applied to a $K_4$-minor graph, the proposed algorithm has obtained ${\chi}(G)=3$ instead of ${\chi}(G)=4$, proving that the Hadwiger conjecture is not universally applicable to all the graphs. The proposed algorithm, however, is a simple algorithm that directly obtains an independent set minor of ${\chi}(G)=k$ to assign an equal color to the vertices of each independent set without having to determine minors in the first place.

• Journal of the Korea Society of Computer and Information
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• v.19 no.5
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• pp.19-25
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• 2014

In this paper, I seek the chromatic number, the maximum number of colors necessary when adjoining vertices in the plane separated apart at the distance of 1 shall receive distinct colors. The upper limit of the chromatic number has been widely accepted as $4{\leq}{\chi}(G){\leq}7$ to which Hadwiger-Nelson proposed ${\chi}(G){\leq}7$ and Soifer ${\chi}(G){\leq}9$ I firstly propose an algorithm that obtains the minimum necessary chromatic number and show that ${\chi}(G)=3$ is attainable by determining the chromatic number for Hadwiger-Nelson's hexagonal graph. The proposed algorithm obtains a chromatic number of ${\chi}(G)=4$ assuming a Hadwiger-Nelson's hexagonal graph of 12 adjoining vertices, and again ${\chi}(G)=4$ for Soifer's square graph of 8 adjoining vertices. assert. Based on the results as such that this algorithm suggests the maximum chromatic number of a planar graph is ${\chi}(G)=4$ using simple assigned rule of polynomial time complexity to color for a vertex with minimum degree.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.167-183
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• 2002

A modified discretization ABS algorithm for solving a class of singular nonlinear systems, F($\chi$)=0, where $\chi$, F $\in$ $R^n$, is presented, constructed by combining a discretization ABS algorithm arid a method of Hoy and Schwetlick (1990). The second order differential operation of F at a point is not required to be calculated directly in this algorithm. Q-quadratic convergence of this algorithm is given.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.31 no.2
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• pp.111-119
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• 2013

It is essential and fundamental to extract boundary information of target object via massive three-dimensional point data acquired from laser scanner. Especially extracting boundary information of manmade features such as buildings is quite important because building is one of the major components consisting complex contemporary urban area, and has artificially defined shape. In this research, extended ${\chi}$-algorithm using geometry information of point data was proposed to extract boundary information of building from three-dimensional point data consisting building. The proposed algorithm begins with composing Delaunay triangulation process for given points and removes edges satisfying specific conditions process. Additionally, to make whole boundary extraction process efficient, we used Sweep-hull algorithm for constructing Delaunay triangulation. To verify the performance of the proposed extended ${\chi}$-algorithm, we compared the proposed algorithm with Encasing Polygon Generating Algorithm and ${\alpha}$-Shape Algorithm, which had been researched in the area of feature extraction. Further, the extracted boundary information from the proposed algorithm was analysed against manually digitized building boundary in order to test accuracy of the result of extracting boundary. The experimental results showed that extended ${\chi}$-algorithm proposed in this research proved to improve the speed of extracting boundary information compared to the existing algorithm with a higher accuracy for detecting boundary information.

• Journal of the Korea Society of Computer and Information
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• v.18 no.11
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• pp.159-165
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• 2013

This paper proposes a O(E) polynomial-time algorithm that has been devised to simultaneously solve edge-coloring problem and graph classification problem both of which remain NP-complete. The proposed algorithm selects an edge connecting maximum and minimum degree vertices so as to determine the number of edge coloring ${\chi}^{\prime}(G)$. Determined ${\chi}^{\prime}(G)$ is in turn either ${\Delta}(G)$ or ${\Delta}(G)+1$. Eventually, the result could be classified as class 1 if ${\chi}^{\prime}(G)={\Delta}(G)$ and as category 2 if ${\chi}^{\prime}(G)={\Delta}(G)+1$. This paper also proves Vizing's planar graph conjecture, which states that 'all simple, planar graphs with maximum degree six or seven are of class one, closing the remaining possible case', which has known to be NP-complete.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.10a
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• pp.223-226
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• 2009

Recently, Mining negative association rules has received some attention and proved to be useful. Negative association rules are useful in market-basket analysis to identify products that conflict with each other or products that complement each other. Several algorithms have been proposed. However, there are some questions with those algorithms, for example, misleading rules will occur when the positive and negative rules are mined simultaneously. The chi-squared test that based on the mature theory and Correlation Coefficient can avoid the problem. In this paper, We proposed the algorithm PNCCR based on chi-squared test and correlation is proposed. The experiment results show that the misleading rules are pruned. It suggests that the algorithm is correct and efficient.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.42 no.4 s.304
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• pp.51-58
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• 2005

This paper proposes a robust scene change detection technique that uses the weighted chi-square test and the automated threshold-decision algorithms. The weighted chi-square test can subdivide the difference values of individual color channels by calculating the color intensities according to NTSC standard, and it can detect the scene change by joining the weighted color intensities to the predefined chi-square test which emphasize the comparative color difference values. The automated threshold-decision at algorithm uses the difference values of frame-to-frame that was obtained by the weighted chi-square test. At first, The Average of total difference values is calculated and then, another average value is calculated using the previous average value from the difference values, finally the most appropriate mid-average value is searched and considered the threshold value. Experimental results show that the proposed algorithms are effective and outperform the previous approaches.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.129-148
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• 1996

This paper propose the inference mechanism for handling linear polynomial constraints called consistency checking algorithm based on the feasibility checking algorithm borrowed from linear pro-gramming. in contrast with other approaches proposed algorithm can efficiently and coherented by linear polynomial forms. The developed algorithm is successfully applied to the symbolic simulation that offers a convenient means to conduct multiple simultaneous exploration of model behaviors.