• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.2
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• pp.429-434
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• 2017

In a graph G=(V, E) with n vertices, there is an unique box which is finally laid on each vertex. Thus each vertex and box is both numbered from 1 to n and the box i should be laid on the vertex i. But, the box ${\pi}$(i) is initially located on the vertex i according to a permutation ${\pi}$. In each step, the robot can walk along an edge of G and can carry at most one box at a time. Also when arriving at a vertex, the robot can swap the box placed there with the box it is carrying. The problem is to minimize the total step so that every vertex has its own box, that is, the shuffled boxes are sorted. In this paper, we shall find an upper bound of the minimum number of steps and show that the movement of the robot is found in $O(n^2)$ time when G is a cycle.

• The Journal of Korean Society for Radiation Therapy
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• v.12 no.1
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• pp.112-116
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• 2000

Purpose : The vertex scalp is always tangentially irradiated during total skin electron beam(TSEB) This study was discuss to the dose distribution at the vertex scalp and to evaluate the use of an electron reflector. positioned above the head as a means of improving the dose uniformity. Methods and Materials Vetex dosimetry was performed using ion-chamber and TLD. Measurements were 6 MeV electron beam obtained by placing an acrylic beam speller in the beam line. Studies were performed to investigate the effect of electron scattering on vertex dose when a lead reflector $40{\times}40cm$ in area, was positioned above the phantom. Results : The surface dose at the vertex, in the without of the reflector was found to be less than $37.8\%$ of the skin dose. Use of the lead reflector increased this value to $62.2\%$ for the 6 MeV beam. Conclusion : The vertex may be significantly under-dosed using standard techniques for total skin electron beam. Use of an electron reflector improves the dose uniformity at the vertex and may reduce or eliminate the need for supplemental irradiation.

• 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.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.223.1-223.1
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• 2005

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.37 no.5
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• pp.84-93
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• 2000

The conventional fractal decoding was implemented to IFS(iterated function system) for every range regions But a part of the range regions can be decoded without the iteration and there is a data dependence regions In order to decode $R{\times}R$ range blocks, It needs $2R{\times}2R$ domain blocks This decoding can be analyzed to the dependence graph The vertex of the graph represents the range blocks, and the vertex is classified into the vertex of the range and domain The edge indicates that the vertex is referred to the other vertices The in-degree and the out-degree are defined to the number of the edge that is entered and exited, respectively The proposed method is analyzed by a dependence graph to the fractal code, and the decoding order is recomposed by the information of the out-degree That is, If the out-degree of the vertex is zero, then this vertex can be used to the vertex with data dependence Thus, the proposed method can extend the data dependence regions by the recomposition of the decoding order As a result, the Iterated regions are minimized without loss of the image quality or PSNR(peak signal-to-noise ratio), Therefore, it can be a fast decoding by the reducing to the computational complexity for IFS in the fractal Image decoding.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.155-167
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• 2007

A graph G is called to be a 2-degree integral subgraph of a q-tree if it is obtained by deleting an edge e from an integral subgraph that is contained in exactly q - 1 triangles. An added-vertex q-tree G with n vertices is obtained by taking two vertices u, v (u, v are not adjacent) in a q-trees T with n - 1 vertices such that their intersection of neighborhoods of u, v forms a complete graph $K_{q}$, and adding a new vertex x, new edges xu, xv, $xv_{1},\;xv_{2},\;{\cdots},\;xv_{q-4}$, where $\{v_{1},\;v_{2},\;{\cdots},\;v_{q-4}\}\;{\subseteq}\;K_{q}$. In this paper we prove that a graph G with minimum degree not equal to q - 3 and chromatic polynomial $$P(G;{\lambda})\;=\;{\lambda}({\lambda}-1)\;{\cdots}\;({\lambda}-q+2)({\lambda}-q+1)^{3}({\lambda}-q)^{n-q-2}$$ with $n\;{\geq}\;q+2$ has and only has 2-degree integral subgraph of q-tree with n vertices and added-vertex q-tree with n vertices.

• Korean Management Science Review
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• v.25 no.2
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• pp.81-88
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• 2008

This paper presents a new algorithm for the K shortest paths problem in a network. After a shortest path is produced with Dijkstra algorithm. detouring paths through inward arcs to every vertex of the shortest path are generated. A length of a detouring path is the sum of both the length of the inward arc and the difference between the shortest distance from the origin to the head vertex and that to the tail vertex. K-1 shorter paths are selected among the detouring paths and put into the set of K paths. Then detouring paths through inward arcs to every vertex of the second shortest path are generated. If there is a shorter path than the current Kth path in the set. this path is placed in the set and the Kth path is removed from the set, and the paths in the set is rearranged in the ascending order of lengths. This procedure of generating the detouring paths and rearranging the set is repeated until the $K^{th}-1$ path of the set is obtained. The computational results for networks with about 1,000,000 nodes and 2,700,000 arcs show that this algorithm can be applied to a problem of generating the detouring paths in the metropolitan traffic networks.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.60-66
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• 2006

This paper presents a new algorithm for the K shortest path problem in a directed network. After a shortest path is produced with Dijkstra algorithm, detouring paths through inward arcs to every vertex of the shortest path are generated. A length of a detouring path is the sum of both the length of the inward arc and the difference between the shortest distance from the origin to the head vertex and that to the tail vertex. K-1 shorter paths are selected among the detouring paths and put into the set of K paths. Then detouring paths through inward arcs to every vertex of the second shortest path are generated. If there is a shorter path than the current Kth path in the set, this path is placed in the set and the Kth path is removed from the set, and the paths in the set is rearranged in the ascending order of lengths. This procedure of generating the detouring paths and rearranging the set is repeated for the K-1 st path of the set. This algorithm can be applied to a problem of generating the detouring paths in the navigation system for ITS and also for vehicle routing problems.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.8
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• pp.999-1007
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• 1999

이 논문은 재귀원형군 G(2^m , 2^k )를 그래프 이론적 관점에서 고찰하고 정점이 서로소인 사이클과 그래프 invariant에 관한 위상 특성을 제시한다. 재귀원형군은 1 에서 제안된 다중 컴퓨터의 연결망 구조이다. 재귀원형군 {{{{G(2^m , 2^k )가 길이 사이클을 가질 필요 충분 조건을 구하고, 이 조건하에서 G(2^m , 2^k )는 가능한 최대 개수의 정점이 서로소이고 길이가l`인 사이클을 가짐을 보인다. 그리고 정점 및 에지 채색, 최대 클릭, 독립 집합 및 정점 커버에 대한 그래프 invariant를 분석한다.Abstract In this paper, we investigate recursive circulant G(2^m , 2^k ) from the graph theory point of view and present topological properties of G(2^m , 2^k ) concerned with vertex-disjoint cycles and graph invariants. Recursive circulant is an interconnection structure for multicomputer networks proposed in 1 . A necessary and sufficient condition for recursive circulant {{{{G(2^m , 2^k ) to have a cycle of lengthl` is derived. Under the condition, we show that G(2^m , 2^k ) has the maximum possible number of vertex-disjoint cycles of length l`. We analyze graph invariants on vertex and edge coloring, maximum clique, independent set and vertex cover.

• Proceedings of the Korea Multimedia Society Conference
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• 2002.05d
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• pp.901-906
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• 2002

This paper is a research about method, that is used in Rapid Prototyping system, that inserts and extracts watermark in STL(standard transform language) that has a 3D geometrical model. The proposed algorithm inserts watermark in the vertex domain of STL facet without the distortion of 3D model. If we make use of a established algorithm for watermarking of STL, a watermark inserted to 3D model can be removed by simple attack that change order of facet. The proposed algorithm has robustness about these attack. Experiment results verify that the proposed algorithm, to encode and decode watermark in STL 3D geometrical model, doesn't distort a 3D model at all. And it shows that the proposed algorithm is available.