• 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 the Korea Institute of Information and Communication Engineering
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• v.21 no.11
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• pp.2103-2108
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• 2017

For n points $p_i$ on the m-dimensional plane $R^m$ and a fixed range r, consider a set $T_i$ containing points the distances from $p_i$ of which are less than or equal to r. In case m=1, $T_i$ is an interval on a line, it is a circle on a plane when m=2. For the vertices corresponding to the sets $T_i$, there is an edge between the vertices if the two sets intersect. Then this graph is called an intersection graph G. For m=1 G is called a proper interval graph and for m=2, it is called an unit disk graph. In this paper, we are concerned in the intersection graph G(r) when r changes. In particular, we consider the problem to find the minimum r such that G(r)is connected. For this problem, we propose an O(n) algorithm for the proper interval graph and an $O(n^2{\log}\;n)$ algorithm for the unit disk graph. For the dynamic environment in which the points on a line are added or deleted, we give an O(log n) algorithm for the problem.

• Journal of Wetlands Research
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• v.15 no.3
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• pp.397-406
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• 2013

Wetland conservation plan has been established to protect ecologically important wetlands based on vegetation integrity, spatial distribution of endangered species, but recently more demands are concentrated on the landscape ecological approaches such as topological relationship, neighboring area, spatial arrangements between wetlands at the broad scale. Landscape ecological analysis and graph theory are conducted to identify spatial characteristics related to core nodes and weak links of wetland networks in Nakdong basin. Regular planar model, which is selected for wetland networks, is applied in the Nakdong basin. The analysis indicates that 5 regional groups and 4 core wetlands are extracted with 15km threshold distance. The IIC and PC values based on the binary and probability models suggest that the wetland group C composed of main stream of Nakdong river and Geumho river is the most important area for wetland network. Wetland conservation plan, restoration projected of damaged and weak links between wetlands should be proposed through evaluating the node, links, and networks from wetlands at the local to the regional scale in Nakdong basin.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.48 no.1
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• pp.33-45
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• 2011

In this paper, we present a method for extracting video objects efficiently by using the modified graph cut algorithm based on contour information. First, we extract objects at the first frame by an automatic object extraction algorithm or the user interaction. To estimate the objects' contours at the current frame, motion information of objects' contour in the previous frame is analyzed. Block-based histogram back-projection is conducted along the estimated contour point. Each color model of objects and background can be generated from back-projection images. The probabilities of links between neighboring pixels are decided by the logarithmic based distance transform map obtained from the estimated contour image. Energy of the graph is defined by predefined color models and logarithmic distance transform map. Finally, the object is extracted by minimizing the energy. Experimental results of various test images show that our algorithm works more accurately than other methods.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.4A
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• pp.364-370
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• 2002

In this paper, we propose a VLSI array architecture for high speed processing of FBMA. First of all, the sequential FBMA is transformed into a single assignment code by using the index space expansion, and then the dependance graph is obtained from it. The two dimensional VLSI array is derived by projecting the dependance graph along the optimal direction. Since the candidate blocks in the search range are overlapped with columns as well as rows, the processing elements of the VLSI array are designed to reuse the overlapped data. As the results, the number of data inputs is reduced so that the processing performance is improved. The proposed VLSI array has (N$^2$+1)${\times}$(2p+1) processing elements and (N+2p) input ports where N is the block size and p is the maximum search range. The computation time of the rat reference block is (N$^2$+2(p+1)N+6p), and the block pipeline period is (3N+4p-1).

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.8
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• pp.1604-1611
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• 2007

In a process of insect footprint recognition, basic footprint segments should be extracted from a whole insect footprint image in order to find out appropriate features for classification. In this paper, we used a clustering method as a preprocessing stage for extraction of basic insect footprint segments. In general, sizes and strides of footprints may be different according to type and sire of an insect for recognition. Therefore we proposed an improved ART2 algorithm for extraction or basic insect footprint segments regardless of size and stride or footprint pattern. In the proposed ART2 algorithm, threshold value for clustering is determined automatically using contour shape of the graph created by accumulating distances between all the spots of footprint pattern. In the experimental results applying the proposed method to two kinds of insect footprint patterns, we could see that all the clustering results were accomplished correctly.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2007.06a
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• pp.275-278
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• 2007

In this paper, we proposed a automatic extraction method as a preprocessing stage for extraction of basic insect footprint segments. In general, sizes and strides of footprints may be different according to type and size of an insect for recognition. Therefore we proposed an improved algorithm for extraction of basic insect footprint segments regardless of size and stride of footprint pattern. In the proposed algorithm, threshold value for clustering is determined automatically using contour shape of the graph created by accumulating distances between all the spots of footprint pattern. In the experimental results applying the proposed method, The basic footprint segments should be extracted from a whole insect footprint image using significant information in order to find out appropriate features for classification.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.7B
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• pp.1239-1251
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• 1999

In this paper a scalable QoS-based hierarchical inter-domain routing scheme for distributed multimedia applications in a high speed wide area network. The problem of QoS-based routing is formulated as a multicriteria shortest path problem, known as NP-complete[21,30]. Our routing scheme consists of two phases. In Phase 1, two graph construction algorithms are performed to model the network under consideration as a graph. The graph contains a part of the network topology which is completely neglected or partially considered by existing routing schemes, thus maintaining more accurate topology information. In Phase 2, a heuristic call-by-call algorithm is performed for selecting a feasible path efficiently in depth first search-like manner on the graph and tailoring to each application's QoS requirements, beginning at a vertex that represents the source node. In this paper, a simple rule is also produced, by which the visiting order of outgoing edges at each vertex on the graph is determined. The rule is based on each edge's the minimum normalized slackness to the QoS requested. The proposed routing scheme extends the PNNI-type hierarchical routing framework. Note that our routing scheme is one of a few QoS-based hierarchical routing schemes that address explicitly the issue of selecting a path with multiple metrics.

• The Mathematical Education
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• v.61 no.3
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• pp.419-439
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• 2022

This study is based on Freudenthal's mathmatising process and the didactical phenomenology of linear function concept, I have described and examined the process in which students represent the constant rate of change into tables, graphs and equations and, in this way, how they construct mental objects and essence of the linear function concept. The students used the proportionality as composite units, when they represented the phenomenon with constant rate of change into tables. When representing in graphs, all but one student represented it into a line. There were differences among the students in the level they were using the given conditions, co-variation perspective, and corresponding rules when formulating equations. The students compared the relationship between two variables in a multiplicative way, and under the guidance of teachers they reached to the understanding that its relationship becomes a constant. Moreover, they could construct mental objects of a constant rate of change, understanding the situation where the relationship between time difference and distance difference becomes one value, namely speed. The students had difficulties in connecting the rate of change with the inclination of a line. The students constructed the essence (concept) of linear functions, after building and organizing the image that the rate of change is constant, the graph is linear, and the equation is formulated as y=ax+b (a: inclination, b: intercept).

• Journal of the Korea Society of Computer and Information
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• v.28 no.4
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• pp.83-91
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• 2023

In this paper, we propose a robustness sensitivity index (RSI) of highway networks to analyze the effect of congestion in a specific section on the entire highway. The newly proposed RSI is defined as the change in the total mileage of the transportation network per extended unit length when the length of a particular section is extended. When the RSI value is large, traffic congestion in the section has a worse effect on the entire network than in other sections. The existing network robustness index (NRI) simply observes changes in transportation networks with and without specific sections, but the RSI proposed in this study is a kind of performance indicator that allows quantitative analysis of the ripple effect of the entire network according to the degree of congestion in a specific section. While changing the degree of congestion in a particular section, it is possible to calculate how the traffic volume increases, decreases, and the size and location of the congestion section change. This analysis proves the superiority of RSI as it cannot be analyzed with NRI. Various properties of RSI are analyzed using data from the domestic highway network. In addition, using the RSI concept, it is shown that the ripple effect on other sections in which a change in the degree of congestion of a specific section occurs can be analyzed.