• Journal of KIISE:Computer Systems and Theory
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• v.27 no.10
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• pp.835-839
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• 2000

보로노이 다이아그램은 계산기하학에서 다양한 형태의 근접 문제를 해결함에 있어 중요한 역할을 하고 있다. 일반적으로 평면상의 n 개의 점에 의한 평면 보로노이 다이아그램 O(nlogn) 시간에 생성할 수 있으며 이 알고리즘의 시간 복잡도가 최적임이 밝혀져 있다. 본 논문에서는 특별한 관계를 갖는 단위 구면상의 점들에 대한 구면 상에서 정의되는 보로노이 다이아그램을 O(n)에 생성하는 알고리즘을 제시한다. 이때 주어진 구면상의 점들은 볼록 다면체의 단위 법선 벡터들의 종점에 해당되며, 구면 보로노이 다이아그램의 선분은 구면상의 geodesic으로 이루어진다.

• Journal of Korea Multimedia Society
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• v.3 no.3
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• pp.298-308
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• 2000

We present an efficient algorithm for finding the sequence of extreme vortices of a moving regular convex polyhedron of with respect to a fixed plane H.. The algorithm utilizes the spherical Voronoi diagram that results from the outward unit normal vectors nF$_{i}$ 's of faces of P. It is well-known that the Voronoi diagram of n sites in the plane can be computed in 0(nlogn) time, and this bound is optimal. However. exploiting the convexity of P, we are able to construct the spherical Voronoi diagram of nF$_{i}$ ,'s in O(n) time. Using the spherical Voronoi diagram, we show that an extreme vertex problem can be transformed to a spherical point location problem. The extreme vertex problem can be solved in O(logn) time after O(n) time and space preprocessing. Moreover, the sequence of extreme vertices of a moving regular convex polyhedron with respect to H can be found in (equation omitted) time, where m$^{j}$ $_{k}$ (1$\leq$j$\leq$s) is the number of edges of a spherical Voronoi region sreg(equation omitted) such that (equation omitted) gives one or more extreme vertices.

• Proceedings of KOSOMES biannual meeting
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• 2017.11a
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• pp.129-129
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• 2017

• Journal of the Korean Institute of Intelligent Systems
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• v.9 no.5
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• pp.490-495
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• 1999

In this paper. a learning method VoD-EBP for neural networks is proposed, which learn patterns by error back propagation. Based on Voronoi diagram, the method initializes the weights of the neural networks systematically, wh~ch results in faster learning speed and alleviated local optimum problem. The method also shows better the reliability of the design of neural network because proper number of hidden nodes are determined from the analysis of Voronoi diagram. For testing the performance, this paper shows the results of solving the XOR problem and the parity problem. The results were showed faster learning speed than ordinary error back propagation algorithm. In solving the problem, local optimum problems have not been observed.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.842-847
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• 2005

Although there are many applications of Euclidean Voronoi diagram for spheres in a 3D space in various disciplines from sciences and engineering, it has not been studied as much as it deserves. In this paper, we present an edge-tracing algorithm to compute the Euclidean Voronoi diagram of 3-dimensional spheres in O(mn) in the worst-case, where m is the number of edges of Voronoi diagram and n is the number of spheres. After building blocks for the algorithm, we show an example of Voronoi diagram for atoms using actual protein data and discuss its applications for protein analysis.