• Title, Summary, Keyword: Prim′s algorithm

### Genetic Algorithm Using-Floating Point Representation for Steiner Tree (스타이너 트리를 구하기 위한 부동소수점 표현을 이용한 유전자 알고리즘)

• 김채주;성길영;우종호
• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.5
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• pp.1089-1095
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• 2004
• The genetic algorithms have been used to take a near optimal solution because The generation of the optimal Steiner tree from a given network is NP-hard problem,. The chromosomes in genetic algorithm are represented with the floating point representation instead of the existing binary string for solving this problem. A spanning tree was obtained from a given network using Prim's algorithm. Then, the new Steiner point was computed using genetic algorithm with the chromosomes in the floating point representation, and it was added to the tree for approaching the result. After repeating these evolving steps, the near optimal Steiner tree was obtained. Using this method, the tree is quickly and exactly approached to the near optimal Steiner tree compared with the existing genetic algorithms using binary string.

### Fast Determination of Minimum Spanning Tree Based on Down-sizing Technique of Edges Population (간선 모집단 규모축소 기법을 적용한 빠른 최소신장트리 결정)

• Lee, Sang-Un;Choi, Myeong-Bok
• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.1
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• pp.51-59
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• 2014
• This paper suggests a method of lessening number of a graph's edges population in order to rapidly obtain the minimum spanning tree. The present minimum spanning tree algorithm works on all the edges of the graph. However, the suggested algorithm reduces the edges population size by means of applying a method of deleting maximum weight edges in advance from vertices with more than 2 valencies. Next, it applies a stopping criterion which ideally terminates Borůvka, Prim, Kruskal and Reverse-Delete algorithms for reduced edges population. On applying the suggested algorithm to 9 graphs, it was able to minimize averagely 83% of the edges that do not become MST. In addition, comparing to the original graph, edges are turned out to be lessened 38% by Borůvka, 37% by Prim, 39% by Kruskal and 73% by Reverse-Delete algorithm, and thereby the minimum spanning tree is obtained promptly.

### Load Balancing Technique to Release Multiple Overloading of Distribution Feeders using Minimum Spanning Tree (최소신장트리를 이용한 배전선로 다중 과부하 해소 방법)

• Oh, Seong-Hyeon;Lee, Han-Seong;Kim, Young-Kook;Lim, Seong-Il
• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.29 no.2
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• pp.33-39
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• 2015
• Power supplying capacity of the distribution feeder should be maintained within thermal capacity of the wire. This paper presents the minimum spanning tree based load balancing technique to release multiple overloading of distribution feeders. In order to minimize number of involved backup feeders, Dijkstra and Prim algorithm are adopted to construct minimum spanning tree. Simulation testing result based on part of KEPCO's commercial distribution systems shows effectiveness of proposed scheme.

### Efficient Construction of Euclidean Minimum Spanning Tree Using Partial Polynomial-Time Approximation Scheme in Unequality Node Distribution (비 균등 노드 분포환경에서 부분 PTAS를 이용한 효과적인 유클리드 최소신장트리 생성)

• Kim, In-Bum;Kim, Soo-In
• Journal of the Korea Society of Computer and Information
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• v.19 no.6
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• pp.71-80
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• 2014
• Employing PTAS to building minimum spanning tree for a large number of equal distribution input terminal nodes can be a effective way in execution time. But applying PTAS to building minimum spanning tree for tremendous unequal distribution node may lead to performance degradation. In this paper, a partial PTAS reflecting the scheme into specific node dense area is presented. In the environment where 90% of 50,000 input terminal nodes stand close together in specific area, approximate minimum spanning tree by our proposed scheme can show about 88.49% execution time less and 0.86%tree length less than by existing PTAS, and about 87.57%execution time less and 1.18% tree length more than by Prim's naive scheme. Therefore our scheme can go well to many useful applications where a multitude of nodes gathered around specific area should be connected efficiently as soon as possible.

### Three Dimensional Euclidean Minimum Spanning Tree for Connecting Nodes of Space with the Shortest Length (공간 노드들의 최단연결을 위한 3차원 유클리드 최소신장트리)

• Kim, Chae-Kak;Kim, In-Bum
• 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.

### Efficient Construction of Euclidean Steiner Minimum Tree Using Combination of Delaunay Triangulation and Minimum Spanning Tree (들로네 삼각망과 최소신장트리를 결합한 효율적인 유클리드 스타이너 최소트리 생성)

• Kim, Inbum
• 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.

### Soft computing-based slope stability assessment: A comparative study

• Kaveh, A.;Hamze-Ziabari, S.M.;Bakhshpoori, T.
• Geomechanics and Engineering
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• v.14 no.3
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• pp.257-269
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• 2018
• Analysis of slope stability failures, as one of the complex natural hazards, is one of the important research issues in the field of civil engineering. Present paper adopts and investigates four soft computing-based techniques for this problem: Patient Rule-Induction Method (PRIM), M5' algorithm, Group Method of data Handling (GMDH) and Multivariate Adaptive Regression Splines (MARS). A comprehensive database consisting of 168 case histories is used to calibrate and test the developed models. Six predictive variables including slope height, slope angle, bulk density, cohesion, angle of internal friction, and pore water pressure ratio were considered to generate new models. The results of test studies are used for feasibility, effectiveness and practicality comparison of techniques with each other, and with the other available well-known methods in the literature. Results show that all methods not only are feasible but also result in better performance than previously developed soft computing based predictive models and tools. It is shown that M5' and PRIM algorithms are the most effective and practical prediction models.

### Hybrid Minimum Spanning Tree Algorithm (하이브리드 최소신장트리 알고리즘)

• Lee, Sang-Un
• The KIPS Transactions:PartA
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• v.17A no.3
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• pp.159-166
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• 2010
• In this paper, to obtain the Minimum Spanning Tree (MST) from the graph with several nodes having the same weight, I applied both Bor$\dot{u}$vka and Kruskal MST algorithms. The result came out to such a way that Kruskal MST algorithm succeeded to obtain MST, but not did the Prim MST algorithm. It is also found that an algorithm that chooses Inter-MSF MWE in the $2^{nd}$ stage of Bor$\dot{u}$vka is quite complicating. The $1^{st}$ stage of Bor$\dot{u}$vka has an advantage of obtaining Minimum Spanning Forest (MSF) with the least number of the edges, and on the other hand, Kruskal MST algorithm has an advantage of always obtaining MST though it deals with all the edges. Therefore, this paper suggests an Hybrid MST algorithm which consists of the merits of both Bor$\dot{u}$vka's $1^{st}$ stage and Kruskal MST algorithm. When applied additionally to 6 graphs, Hybrid MST algorithm has a same effect as that of Kruskal MST algorithm. Also, comparing the algorithm performance speed and capacity, Hybrid MST algorithm has shown the greatest performance Therefore, the suggested algorithm can be used as the generalized MST algorithm.

### A-PEGASIS : Advanced Power Efficient GAthering in Sensor Information Systems (개선된 센서 라우팅 방식 : A-PEGASIS)

• Suh, Chang-Jin;Yang, Jin-Ung
• Journal of KIISE:Information Networking
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• v.34 no.6
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• pp.458-465
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• 2007
• Wireless Sensor Network(WSN) is a special network that collects measured data by sensor nodes in the predefined sensor field and forwards them to the base station in a distance using their own routing scheme. WSN requires routing techniques to maximize energy efficiency because sensor nodes have non-rechargeable and thus limited energy. Characteristics of WSN are various according to applications, many of routing algorithms have been proposed. This paper proposes an algorithm called A-PEGASIS that basically bases on PEGASIS and enhances in two aspects - an elegant chain generation algorithm and periodical update of chains. We compare performance of the previous algorithm of LEACH, PEGASIS, PEDAP and PEDAP-PA with ours through simulation. It confirms that the A-PEGASIS is most superior in terms of average WSN lifetime and high probability of node survival rate during WSN life time.

### An Ant Colony Optimization Algorithm to Solve Steiner Tree Problem (스타이너 트리 문제를 위한 Ant Colony Optimization 알고리즘의 개발)

• Seo, Min-Seok;Kim, Dae-Cheol
• Journal of the Korean Operations Research and Management Science Society
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• v.33 no.3
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• pp.17-28
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• 2008
• The Steiner arborescence problem is known to be NP-hard. The objective of this problem is to find a minimal Steiner tree which starts from a designated node and spans all given terminal nodes. This paper proposes a method based on a two-step procedure to solve this problem efficiently. In the first step, graph reduction rules eliminate useless nodes and arcs which do not contribute to make an optimal solution. In the second step. ant colony algorithm with use of Prim's algorithm is used to solve the Steiner arborescence problem in the reduced graph. The proposed method based on a two-step procedure is tested in the five test problems. The results show that this method finds the optimal solutions to the tested problems within 50 seconds. The algorithm can be applied to undirected Steiner tree problems with minor changes. 18 problems taken from Beasley are used to compare the performances of the proposed algorithm and Singh et al.'s algorithm. The results show that the proposed algorithm generates better solutions than the algorithm compared.