• Journal of Korean Society of Industrial and Systems Engineering
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• v.45 no.3
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• pp.57-65
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• 2022

DEA(data envelopment analysis) is a technique for evaluation of relative efficiency of decision making units (DMUs) that have multiple input and output. A DEA model measures the efficiency of a DMU by the relative position of the DMU's input and output in the production possibility set defined by the input and output of the DMUs being compared. In this paper, we proposed several DEA models measuring the multi-period efficiency of a DMU. First, we defined the input and output data that make a production possibility set as the spanning set. We proposed several spanning sets containing input and output of entire periods for measuring the multi-period efficiency of a DMU. We defined the production possibility sets with the proposed spanning sets and gave DEA models under the production possibility sets. Some models measure the efficiency score of each period of a DMU and others measure the integrated efficiency score of the DMU over the entire period. For the test, we applied the models to the sample data set from a long term university student training project. The results show that the suggested models may have the better discrimination power than CCR based results while the ranking of DMUs is not different.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.365-379
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• 2005

The purpose of this paper is to correct erroneous proofs of theorems of He, Lu, Wang and Zheng [1] about the topological pressure of continuous flows without fixed points and to give proofs of some results which are stated in the literature without proofs and thereby to show that their theorems are still true.

• Journal of the Korea Society of Computer and Information
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• v.20 no.3
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• pp.107-113
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• 2015

This paper presents a polynomial time algorithm to the minimum cardinality feedback edge set and minimum weight feedback edge set problems. The algorithm makes use of the property wherein the sum of the minimum spanning tree edge set and the minimum feedback edge set equals a given graph's edge set. In other words, the minimum feedback edge set is inherently a complementary set of the former. The proposed algorithm, in pursuit of the optimal solution, modifies the minimum spanning tree finding Kruskal's algorithm so as to arrange the weight of edges in a descending order and to assign cycle-deficient edges to the maximum spanning tree edge set MXST and cycle-containing edges to the feedback edge set FES. This algorithm runs with linear time complexity, whose execution time corresponds to the number of edges of the graph. When extensively tested on various undirected graphs both with and without the weighed edge, the proposed algorithm has obtained the optimal solutions with 100% success and accuracy.

• Proceedings of the Korean Information Science Society Conference
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• 2006.10a
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• pp.494-499
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• 2006

Given a set S of n points in the plane, a minimum-dilation spanning tree of S is a tree with vertex set S of smallest possible dilation. We show that given a set S of n points and a dilation $\delta$ > 1, it is NP-hard to determine whether a spanning tree of S with dilation at most $\delta$ exists.

• Journal of Korean Institute of Industrial Engineers
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• v.31 no.1
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• pp.10-19
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• 2005

The minimum spanning tree (MST) problem is one of the traditional optimization problems. Unlike the MST, the degree constrained minimum spanning tree (DCMST) of a graph cannot, in general, be found using a polynomial time algorithm. So, finding the DCMST of a graph is a well-known NP-hard problem of importance in communications network design, road network design and other network-related problems. So, it seems to be natural to use evolutionary algorithms for solving DCMST. Especially, when applying an evolutionary algorithm to spanning tree problems, a representation and search operators should be considered simultaneously. This paper introduces a new tree representation scheme and a genetic operator for solving combinatorial tree problem using evolutionary algorithms. We performed empirical comparisons with other tree representations on several test instances and could confirm that the proposed method is superior to other tree representations. Even it is superior to edge set representation which is known as the best algorithm.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.5_6
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• pp.319-323
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• 2003

Let P be a set of n points in the plane. A minimum spanning tree(MST) is a spanning tree connecting n points of P such that the sum of lengths of edges of the tree is minimized. A diameter of a tree is the maximum length of paths connecting two points of a spanning tree of P. The problem considered in this paper is to compute the spanning tree whose diameter is minimized over all spanning trees of P. We call such tree a minimum-diameter spanning tree(MDST). The best known previous algorithm[3] finds MDST in $O(n^2)$ time. In this paper, we suggest an approximation algorithm to compute a spanning tree whose diameter is no more than 5/4 times that of MDST, running in O(n$^2$log$^2$n) time. This is the first approximation algorithm on the MDST problem.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.1_2
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• pp.78-85
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• 2004

Given a set S of n points in the plane, a minimum-diameter spanning tree(MDST) for the set might have a degree up to n-1. This might cause the degradation of the network performance because the node with high degree should handle much more requests than others relatively. Thus it is important to construct a spanning tree network with small degree and diameter. This paper presents an algorithm to construct a spanning tree for S satisfying the following four conditions: (1) the degree is controled as an input, (2) the tree diameter is no more than constant times the diameter of MDST, (3) the tree is monotone (even if arbitrary point is fixed as a root of the tree) in the sense that the Euclidean distance from the root to any node on the path to any leaf node is not decreasing, and (4) there are no crossings between edges of the tree. The monotone property will play a role as an aesthetic criterion in visualizing the tree in the plane.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.24 no.68
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• pp.21-30
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• 2001

The purpose of this study is to present methods for determining the k most vital arcs (k-MVAs) in the minimum spanning tree problem(MSTP) using evolutionary algorithms. The problem of finding the k-MVAs in MSTP is to find a set of k arcs whose simultaneous removal from the network causes the greatest increase in the total length of minimum spanning tree. Generally, the problem which determine the k-MVAs in MSTP has known as NP-hard. Therefore, in order to deal with the problem of real world the heuristic algorithms are needed. In this study we propose to three genetic algorithms as the heuristic methods for finding the k-MVAs in MSTP. The algorithms to be presented in this study are developed using the library of the evolutionary algorithm framework(EAF) and the performance of the algorithms are analyzed through the computer experiment.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.225-236
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• 2009

The equicontinuity and scattering properties of continuous semi-flows are studied on a compact metric space. The main results are obtained as follows: first, the complexity function defined by the spanning set is bounded if and only if the system is equicontinuous; secondly, if a continuous semi-flow is topologically weak mixing, then it is pointwise scattering; thirdly, several equivalent conditions for the time-one map of a continuous semi-flow to be scattering are presented; Finally, for a minimal continuous map it is shown that the "non-dense" requirement is unnecessary in the definition of scattering by using open covers.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.967-983
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• 2010

Let M be an n-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-{\kappa}^2$. Using the cone total curvature TC($\Gamma$) of a graph $\Gamma$ which was introduced by Gulliver and Yamada [8], we prove that the density at any point of a soap film-like surface $\Sigma$ spanning a graph $\Gamma\;\subset\;M$ is less than or equal to $\frac{1}{2\pi}\{TC(\Gamma)-{\kappa}^2Area(p{\times}\Gamma)\}$. From this density estimate we obtain the regularity theorems for soap film-like surfaces spanning graphs with small total curvature. In particular, when n = 3, this density estimate implies that if $TC(\Gamma)$ < $3.649{\pi}\;+\;{\kappa}^2\inf\limits_{p{\in}F}Area(p{\times}{\Gamma})$, then the only possible singularities of a piecewise smooth (M, 0, $\delta$)-minimizing set $\Sigma$ are the Y-singularity cone. In a manifold with sectional curvature bounded above by $b^2$ and diameter bounded by $\pi$/b, we obtain similar results for any soap film-like surfaces spanning a graph with the corresponding bound on cone total curvature.