• 전기의세계
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• 제30권5호
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• pp.297-305
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• 1981

The problem of finding shortest paths between every pair of points in a network is solved employing and optimal network decomposition in which the network is decomposed into a number of subnetworks minimizing the number of cut-set between them while each subnetwork is constrained by a size limit. Shortest path computations are performed on individual subnetworks, and the solutions are recomposed to obtain the solution of the original network. The method when applied to large scale networks significantly reduces core requirement and computation time. This is demonstrated by developing a computer program based on the method and applying it to 30-vertex, 160-vertex, and 273-vertex networks.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권1호
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• pp.57-61
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• 2002

Let G be a connected graph. A pebbling move on a graph G is the movement of taking two pebbles off from a vertex and placing one of them onto an adjacent vertex. The pebbling number f(G) of a connected graph G is the least n such that any distribution of n pebbles on the vertices of G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. In this paper, the pebbling numbers of the compositions of two graphs are computed.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.387-401
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• 2001

If the distance between two vertices becomes longer after the removal of a vertex u, then u is called a hinge vertex. In this paper, a linear time sequential algorithm is presented to find all hinge vertices of an interval graph. Also, a parallel algorithm is presented which takes O(n/P + log n) time using P processors on an EREW PRAM.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.141-154
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• 2007

The connectivity problem is a fundamental problem in graph theory. The best known algorithm to solve the connectivity problem on general graphs with n vertices and m edges takes $O(K(G)mn^{1.5})$ time, where K(G) is the vertex connectivity of G. In this paper, an efficient algorithm is designed to solve vertex connectivity problem, which takes $O(n^2)$ time and O(n) space for a trapezoid graph.

• 충청수학회지
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• 제14권1호
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• pp.7-14
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• 2001

Let G be a connected graph. A pebbling move on a graph G is taking two pebbles off one vertex and placing one of them on an adjacent vertex. The pebbling number of a connected graph G, f(G), is the least n such that any distribution of n pebbles on the vertices of G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. In this paper, the pebbling numbers of the lexicographic products of some graphs are computed.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.339-358
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• 2021

Zagreb indices and their modified versions of a molecular graph are important descriptors which can be used to characterize the structural properties of organic molecules from different aspects. In this work, we investigate some properties of the modified second multiplicative Zagreb index of graphs with given connectivity. In particular, we obtain the maximum values of the modified second multiplicative Zagreb index with fixed number of cut edges, or cut vertices, or edge connectivity, or vertex connectivity of graphs. Furthermore, we characterize the corresponding extremal graphs.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 1999년도 가을 학술발표논문집 Vol.26 No.2 (2)
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• pp.595-597
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• 1999

기존의 LOD 제어방법들은 랜더링속도를 성공적으로 증가시켜왔으나 오버헤드가 크다는 단점을 갖고 있다. 이러한 오버헤드는 각 vertex마다 view-frustum clipping, back-face culling, 스크린 공간 기하학적 오차계산과 같은 view-dependent refinement criteria를 측정하고, 메쉬의 LOD를 바꾸기 위해서 edge collapse/vertex split를 수행하기 때문이다. 제안하는 방법은 메쉬를 여러 개의 region들로 나누고 vertex가 아닌 region에 대해 view-dependent refinement criteria를 측정하므로 오버헤드가 훨씬 작다. 또한 각 region 들의 LOD가 바뀔 때 미리 만들어 둔 LOD 버전들중에서 하나를 선택하기만 하면 되므로, edge collapse/vertex split을 수행하는 오버헤드는 없다. 실험적으로 제안하는 LOD 제어방법은 기존의 방법들보다 작은 메모리를 사용하고 LOD 제어 오버헤드도 적으며, LOD 제어를 하지 않은 경우보다 2배-5배의 랜더링 속도향상을 얻었다.

• 한국정밀공학회지
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• 제22권9호
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• pp.202-211
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• 2005

This paper introduces and illustrates the results of a new method fer offsetting triangular mesh by moving all vertices along the multiple normal vectors of a vertex. The multiple normal vectors of a vertex are set the same as the normal vectors of the faces surrounding the vertex, while the two vectors with the smallest difference are joined repeatedly until the difference is smaller than allowance. Offsetting with the multiple normal vectors of a vertex does not create a gap or overlap at the smooth edges, thereby making the mesh size uniform and the computation time short. In addition, this offsetting method is accurate at the sharp edges because the vertices are moved to the normal directions of faces and joined by the blend surface. The method is also useful for rapid prototyping and tool path generation if the triangular mesh is tessellated part of the solid models with curved surfaces and sharp edges. The suggested method and previous methods are implemented on a PC using C++ and illustrated using an OpenGL library.

• 한국HCI학회:학술대회논문집
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• 한국HCI학회 2009년도 학술대회
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• pp.475-481
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• 2009

실시간 렌더링에서 Fur는 모피등과 같이 매우 복잡한 표면을 표현하는 문제로 가상세계의 사실감을 높이는데 매우 중요한 요소이다. 복잡한 Fur의 실시간 렌더링을 위하여 다수의 방법이 제안되어 왔으나, Fur를 사실처럼 보여지게 하는 측면에서, 기존의 정적인 표현으로서는 한계점이 존재한다. 본 논문에서는 중력 및 외력에 의한 시뮬레이션을 통한 Fur의 실시간 Animation 방법을 제안한다. 기본 구조는 모피의 볼륨을 구성하는 n개의 Shell과 Shell의 표현을 보강하는 Fin의 구조로 이루어져 있고, Shell과 Fin의 공유 Vertex 배열을 통해 이 두 가지 구조를 하나로 통합한다. 이 공유 Vertex 배열에 본 논문에서 제안하는 중력 및 외력에 의한 시뮬레이션을 적용하여 공유 Vertex 배열을 변형시킨다. 이 후 변형된 공유 Vertex배열을 기반으로 Rendering을 수행하게 된다. 본 논문에서 제안하는 방법을 사용하여, 정적인 Fur Rendering이 아닌 동적으로 움직이는 Fur Rendering을 사용 함 으로써 좀 더 높은 현실감을 느낄 수 있을 것으로 기대한다.

• 전기학회논문지P
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• 제53권4호
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• pp.210-215
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• 2004

This paper proposes an implicit method for computing the minimum cost feedback vertex set for a graph. For an arbitrary graph, a Boolean function is derived, whose satisfying assignments directly correspond to feedback vertex sets of the graph. Importantly, cycles in the graph are never explicitly enumerated, but rather, are captured implicitly in this Boolean function. This function is then used to determine the minimum cost feedback vertex set. Even though computing the minimum cost satisfying assignment for a Boolean function remains an NP-hard problem, it is possible to exploit the advances made in the area of Boolean function representation in logic synthesis to tackle this problem efficiently in practice for even reasonably large sized graphs. The algorithm has obvious application in flip-flop selection for partial scan. The algorithm proposed in this paper is the first to obtain the MFVS solutions for many benchmark circuits.