• 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.

• Proceedings of the Korean Information Science Society Conference
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• 2003.04a
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• pp.806-808
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• 2003

이차원 평면에 주어진 n 개의 점을 연결하는 신장 트리(spanning tree) 중에서, 지름이 최소가 되는 최소지름 신장 트리는 특정 점에서의 분지수가 n-1 까지 증가할 수 있다. 본 논문에서는 트리의 분지수(degree)를 입력으로 받아 그 분지수를 넘지 않는 신장 트리를 구성하면서 트리의 지름은 최소 지름의 상수 배를 넘지 않도록 하는 구성 방법을 제안한다.

• 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 the Korea Society of Computer and Information
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• v.19 no.1
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• pp.57-64
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• 2014

As Steiner minimum tree building belongs to NP-Complete problem domain, heuristics for the problem ask for immense amount execution time and computations in numerous inputs. In this paper, we propose an efficient mechanism of euclidean Steiner minimum tree construction for numerous inputs using combination of Delaunay triangulation and Prim's minimum spanning tree algorithm. Trees built by proposed mechanism are compared respectively with the Prim's minimum spanning tree and minimums spanning tree based Steiner minimum tree. For 30,000 input nodes, Steiner minimum tree by proposed mechanism shows about 2.1% tree length less and 138.2% execution time more than minimum spanning tree, and does about 0.013% tree length less and 18.9% execution time less than minimum spanning tree based Steiner minimum tree in experimental results. Therefore the proposed mechanism can work moderately well to many useful applications where execution time is not critical but reduction of tree length is a key factor.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.10a
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• pp.496-499
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• 2008

현재 정보영재 교육에서 중요성이 증대되는 사고력 신장 교육에 적합한 교수-학습 프로그램이 부족한 실정이다. 따라서 이 논문에서는 정보영재의 교육과정에 실제적으로 적용할 수 있는 교수-학습 모형을 제시한다. 정보영재 사고력 신장을 위한 영역별 교육 내용에 공통적으로 포함되는 문제들을 분석하여 사고력 신장에 적합한 교육 프로그램 모형으로서 OR 트리에 기반을 둔 교수-학습 모형을 제시한다. 이 논문에서 제시된 OR 트리형 교수-학습 모형을 정보영재의 현장 지도에 도입하기 위하여 8-puzzle 문제를 예로 들어 적용 방안을 제시하며, 적용 결과를 분석하여 교육 프로그램 개발의 타당성을 검증한다. OR 트리형 교수-학습 모형에서는 정보영재의 사고력 신장을 위한 교육 과정에서 주요 내용이 되는 backtracking과 heuristic 개념을 배우며 트리의 탐색 방법들을 익히게 된다.

• Journal of the Korea Society of Computer and Information
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• v.17 no.1
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• pp.161-169
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• 2012

In general, Euclidean minimum spanning tree is a tree connecting input nodes with minimum connecting cost. But the tree may not be optimal when applied to real world problems of three dimension. In this paper, three dimension Euclidean minimum spanning tree is proposed, connecting all input nodes of 3-dimensional space with minimum cost. In experiments for 30,000 input nodes with 100% space ratio, the tree produced by the proposed method can reduce 90.0% connection cost tree, compared with the tree by two dimension Prim's minimum spanning tree. In two dimension plane, the proposed tree increases 251.2% connecting cost, which is pointless in 3-dimensional real world. Therefore, the proposed method can work well for many connecting problems in real world space of three dimensions.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.10a
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• pp.479-482
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• 2008

사고력 신장 교육은 정보영재를 위한 교육과정 및 내용 중에서 매우 중요한 목표이다. 이 논문에서는 정보영재 교육에서 중요성이 증대되는 사고력 신장 교육에 적합한 교수-학습 프로그램을 제시하여 적용하고 분석하는 방안을 마련한다. 사고력 신장 교육을 구성하는 영역별 교육 내용에 포함되는 여러 가지의 문제들에 공통적으로 적용할 수 있는 모형으로서 AND/OR 트리에 기반을 둔 교수-학습 모형을 제시한다. 이 논문에서 제시된 AND/OR 트리형 교수-학습 모형을 정보영재의 현장 교육에 도입하기 위하여 tic-tac-toe 게임 문제를 예로 들어 적용 방안을 제시하며, 그 적용 결과를 분석하여 교육 프로그램 개발의 타당성을 검증한다. AND/OR 트리형 교수-학습 모형에서는 AND 트리와 OR 트리가 결합된 형태의 트리 구성과 그에 따른 트리 탐색을 주요 학습 내용으로 하는 고도의 사고력을 필요로 하는 학습 단계를 필요로 한다.

• KIPS Transactions on Computer and Communication Systems
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• v.2 no.5
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• pp.191-198
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• 2013

It is required to transmit data through shorter path between sensor and base node for real time intrusion detection in wireless sensor networks (WSN) with a mobile base node. Because minimum Wiener index spanning tree (MWST) based routing approach guarantees lower average hop count than that of minimum spanning tree (MST) based routing method in WSN, it is known that MWST based routing is appropriate for real time intrusion detection. However, the minimum Wiener index spanning tree problem which aims to find a spanning tree which has the minimum Wiener index from a given weighted graph was proved to be a NP-hard. And owing to its high dependency on certain nodes, minimum Wiener index tree based routing method has a shorter network lifetime than that of minimum spanning tree based routing method. In this paper, we propose a multi-objective ant colony optimization algorithm to tackle these problems, so that it can be used to detect intrusion in real time in wireless sensor networks with a mobile base node. And we compare the results of our proposed method with MST based routing and MWST based routing in respect to average hop count, network energy consumption and network lifetime by simulation.

• The KIPS Transactions:PartA
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• v.16A no.6
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• pp.509-518
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• 2009

In this paper, a mechanism that produces an approximation edges minimum spanning tree swiftly using virtual nodes called portals dividing given edges into same distance sub-edges. The approximation edges minimum spanning tree can be used in many useful areas as connecting communication lines, road networks and railroad systems. For 3000 random input edges, when portal distance is 0.3, tree building time decreased 29.74% while the length of the produced tree increased 1.8% comparing with optimal edge minimum spanning tree in our experiment. When portal distance is 0.75, tree building time decreased 39.96% while the tree length increased 2.96%. The result shows this mechanism might be well applied to the applications that may allow a little length overhead, but should produce an edge connecting tree in short time. And the proposed mechanism can produce an approximation edge minimum spanning tree focusing on tree length or on building time to meet user requests by adjusting portal distance or portal discard ratio as parameter.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.5A
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• pp.466-473
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• 2010

Several protocols which are based on tree topology to guarantee the important metrics such as energy efficiency in sensor networks have been proposed. However, studies on the effect of topologies in sensor networks, where base node has a high mobility, are very few. In this paper, we propose a minimum Wiener index tree as a suitable topology to the wireless sensor networks with high mobile base node. The minimum Wiener index spanning tree problem which aims to find a tree with minimum Wiener index from a given weighted graph was proved to be NP-hard. We designed a branch and bound algorithm for this problem. To evaluate the performance of proposed tree, the comparisons with minimum spanning tree in terms of transmission distance, energy consumption during one round, and network lifetime was performed by simulations. Our proposed tree outperformed in transmission distance and energy efficiency but underperformed in lifetime.