• Title/Summary/Keyword: Edge Minimum Spanning Tree

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Efficient Connection of Migration Routes with Their Weights Using EGOSST (EGOSST를 이용한 이동 경로의 가중치를 반영한 효과적 연결)

  • Kim, In-Bum
    • The KIPS Transactions:PartA
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    • v.18A no.5
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    • pp.215-224
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    • 2011
  • In this paper, a mechanism connecting all weighted migration routes with minimum cost with EGOSST is proposed. Weighted migration routes may be converted to weighted input edges considered as not only traces but also traffics or trip frequencies of moving object on communication lines, roads or railroads. Proposed mechanism can be used in more wide and practical area than mechanisms considering only moving object traces. In our experiments, edge number, maximum weight for input edges, and detail level for grid are used as input parameters. The mechanism made connection cost decrease average 1.07% and 0.43% comparing with the method using weight minimum spanning tree and weight steiner minimum tree respectively. When grid detail level is 0.1 and 0.001, while each execution time for a connecting solution increases average 97.02% and 2843.87% comparing with the method using weight minimum spanning tree, connecting cost decreases 0.86% and 1.13% respectively. This shows that by adjusting grid detail level, proposed mechanism might be well applied to the applications where designer must grant priority to reducing connecting cost or shortening execution time as well as that it can provide good solutions of connecting migration routes with weights.

Generalized Borůvka's Minimum Spanning Tree Algorithm (일반화된 Borůvka 최소신장트리 알고리즘)

  • Choi, Myeong-Bok;Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.12 no.6
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    • pp.165-173
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    • 2012
  • Given a connected, weighted, and undirected graph, the Minimum Spanning Tree (MST) should have minimum sum of weights, connected all vertices, and without any cycle taking place. Borůvka Algorithm is firstly suggested as an algorithm to evaluate the MST, but it is not widely used rather than Prim and Kruskal algorithms. Borůvka algorithm selects the Minimum Weight Edge (MWE) from each vertex with distinct weights in $1^{st}$ stage, and selects the MWE from each MSF (Minimum Spanning Forest) in $2^{nd}$ stage. But the cycle check and the number of MSF in $1^{st}$ stage and $2^{nd}$ stage are difficult to implication by computer program even if it is easy to verify visually. This paper suggests the generalized Borůvka Algorithm, This algorithm selects all of the same MWEs for each vertex, then checks the cycle and constructs MSF for ascending sorted MWEs. Kruskal method bring into this process. if the number of MSF greats then 1, this algorithm selects MWE from ascending sorted inter-MSF edges. The generalized Borůvka algorithm is verified its application by being applied to the 7 graphs with the many minimum weights or distinct weight edges for any vertex. As a result, the generalized Borůvka algorithm is less required for cycle verification then the Kruskal algorithm. Therefore, the generalized Borůvka algorithm is more fast to obtain MST then Kruskal algorithm.

An Eulerian Cycle Algorithm for Chinese Postman Problem

  • Lee, Sang-Un
    • Journal of the Korea Society of Computer and Information
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    • v.21 no.7
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    • pp.47-52
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    • 2016
  • This paper introduces an algorithm to construct an Eulerian cycle for Chinese postman problem. The Eulerian cycle is formed only when all vertices in the graph have an even degree. Among available algorithms to the Eulerian cycle problem, Edmonds-Johnson's stands out as the most efficient of its kind. This algorithm constructs a complete graph composed of shortest path between odd-degree vertices and derives the Eulerian cycle through minimum-weight complete matching method, thus running in $O({\mid}V{\mid}^3)$. On the contrary, the algorithm proposed in this paper selects minimum weight edge from edges incidental to each vertex and derives the minimum spanning tree (MST) so as to finally obtain the shortest-path edge of odd-degree vertices. The algorithm not only runs in simple linear time complexity $O({\mid}V{\mid}log{\mid}V{\mid})$ but also obtains the optimal Eulerian cycle, as the implementation results on 4 different graphs concur.

Minimum Spanning Tree with Select-and-Delete Algorithm (선택-삭제 최소신장트리 알고리즘)

  • Choi, Myeong-Bok;Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.13 no.4
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    • pp.107-116
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    • 2013
  • This algorithm suggests a method in which a minimum spanning tree can be obtained fast by reducing the number of an algorithm execution. The suggested algorithm performs a select-and-delete process. In the select process, firstly, it performs Borůvka's first stage for all the vertices of a graph. Then it re-performs Borůvka's first stage for specific vertices and reduces the population of the edges. In the delete process, it deletes the maximum weight edge if any cycle occurs between the 3 edges of the edges with the reduced population. After, among the remaining edges, applying the valency concept, it gets rid of maximum weight edges. Finally, it eliminates the maximum weight edges if a cycle happens among the vertices with a big valency. The select-and-delete algorithm was applied to 9 various graphs and was evaluated its applicability. The suggested select process is believed to be the vest way to choose the edges, since it showed that it chose less number of big edges from 6 graphs, and only from 3 graphs, comparing to the number of edges that is to be performed when using MST algorithm. When applied the delete process to Kruskal algorithm, the number of performances by Kruskal was less in 6 graphs, but 1 more in each 3 graph. Also, when using the suggested delete process, 1 graph performed only the 1st stage, 5 graphs till 2nd stage, and the remaining till 3rd stage. Finally, the select-and-delete algorithm showed its least number of performances among the MST algorithms.

Improved Minimum Spanning Tree based Image Segmentation with Guided Matting

  • Wang, Weixing;Tu, Angyan;Bergholm, Fredrik
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.16 no.1
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    • pp.211-230
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    • 2022
  • In image segmentation, for the condition that objects (targets) and background in an image are intertwined or their common boundaries are vague as well as their textures are similar, and the targets in images are greatly variable, the deep learning might be difficult to use. Hence, a new method based on graph theory and guided feathering is proposed. First, it uses a guided feathering algorithm to initially separate the objects from background roughly, then, the image is separated into two different images: foreground image and background image, subsequently, the two images are segmented accurately by using the improved graph-based algorithm respectively, and finally, the two segmented images are merged together as the final segmentation result. For the graph-based new algorithm, it is improved based on MST in three main aspects: (1) the differences between the functions of intra-regional and inter-regional; (2) the function of edge weight; and (3) re-merge mechanism after segmentation in graph mapping. Compared to the traditional algorithms such as region merging, ordinary MST and thresholding, the studied algorithm has the better segmentation accuracy and effect, therefore it has the significant superiority.

Maximum Node Interconnection by a Given Sum of Euclidean Edge Lengths

  • Kim, Joonmo;Oh, Jaewon;Kim, Minkwon;Kim, Yeonsoo;Lee, Jeongeun;Han, Sohee;Hwang, Byungyeon
    • Journal of information and communication convergence engineering
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    • v.17 no.4
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    • pp.246-254
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    • 2019
  • This paper proposes a solution to the problem of finding a subgraph for a given instance of many terminals on a Euclidean plane. The subgraph is a tree, whose nodes represent the chosen terminals from the problem instance, and whose edges are line segments that connect two corresponding terminals. The tree is required to have the maximum number of nodes while the length is limited and is not sufficient to interconnect all the given terminals. The problem is shown to be NP-hard, and therefore a genetic algorithm is designed as an efficient practical approach. The method is suitable to various probable applications in layout optimization in areas such as communication network construction, industrial construction, and a variety of machine and electronics design problems. The proposed heuristic can be used as a general-purpose practical solver to reduce industrial costs by determining feasible interconnections among many types of components over different types of physical planes.

최소신장트리를 이용한 흑점군 자동분석 프로그램 개발

  • Park, Jong-Yeop;Mun, Yong-Jae;Choe, Seong-Hwan
    • The Bulletin of The Korean Astronomical Society
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    • v.37 no.2
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    • pp.130.2-130.2
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    • 2012
  • 태양의 활동영역에서 관측할 수 있는 흑점은 주로 흑점군으로 관측되며, 태양폭발현상의 발생을 예보하기 위한 중요한 관측 대상 중 하나이다. 현재 태양 폭발을 예보하는 모델들은 McIntosh 흑점군 분류법을 사용하며 통계적 모델과 기계학습 모델로 나누어진다. 컴퓨터는 흑점군의 형태학적 특성을 연속적인 값으로 계산하지만 흑점군의 형태적 다양성으로 인해 McIntosh 분류를 잘못 분류할 수도 있다. 이러한 이유로 컴퓨터가 계산한 흑점군의 형태학적인 특성을 예보에 직접 적용하는 것이 필요하다. 우리는 흑점군의 형태학적인 특성(개수, 면적, 면적비 등)과 함께 모든 흑점을 정점(Vertex)으로 하고 그 사이를 연결하는 간선(Edge)으로 하는 간선의 거리 합이 최소인 최소신장트리(Minimum spanning tree : MST)를 작성하였다. 이 최소신장트리를 사용하여 흑점군을 검출하고 가장 면적이 큰 정점을 중심으로 트리의 깊이(Depth)와 차수(Degree)를 계산하였다. 이 방법을 2003년 SOHO/MDI의 태양 가시광 영상에 적용하여 구한 흑점군의 내부 흑점수와 면적은 NOAA에서 산출한 값들과 90%, 99%의 좋은 상관관계를 가졌다. 우리는 이 연구를 통해 흑점군의 형태학적인 특성과 더불어 예보에 직접적으로 활용할 수 있는 방법을 논의하고자 한다.

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Development of an Automatic Program to Analyze Sunspot Groups for Solar Flare Forecasting (태양 플레어 폭발 예보를 위한 흑점군 자동분석 프로그램 개발)

  • Park, Jongyeob;Moon, Yong-Jae;Choi, SeongHwan;Park, Young-Deuk
    • The Bulletin of The Korean Astronomical Society
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    • v.38 no.2
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    • pp.98-98
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    • 2013
  • 태양의 활동영역에서 관측할 수 있는 흑점은 주로 흑점군으로 관측되며, 태양폭발현상의 발생을 예보하기 위한 중요한 관측 대상 중 하나이다. 현재 태양 폭발을 예보하는 모델들은 McIntosh 흑점군 분류법을 사용하며 통계적 모델과 기계학습 모델로 나누어진다. 컴퓨터는 흑점군의 형태학적 특성을 연속적인 값으로 계산하지만 흑점군의 형태적 다양성으로 인해 McIntosh 분류법과 일치하지 않는 경우가 있다. 이러한 이유로 컴퓨터가 계산한 흑점군의 형태학적인 특성을 예보에 직접 적용하는 것이 필요하다. 우리는 흑점군을 검출하기 위해 최소신장트리(Minimum spanning tree : MST)를 이용한 계층적 군집화 기법을 수행하였다. 그래프(Graph)이론에서 최소신장트리는 정점(Vertex)과 간선(Edge)으로 구성된 간선의 가중치의 합이 최소인 트리이다. 우리는 모든 흑점을 정점, 그들의 연결을 간선으로 적용하여 최소신장트리를 작성하였다. 또한 최소신장트리를 활용한 계층적 군집화기법은 초기값에 따른 군집화 결과의 차이가 없기 때문에 흑점군 검출에 있어서 가장 적합한 알고리즘이다. 이를 통해 흑점군의 기본적인 형태학적인 특성(개수, 면적, 면적비 등)을 계산하고 최소신장트리를 통해 가장 면적이 큰 흑점을 중심으로 트리의 깊이(Depth)와 차수(Degree)를 계산하였다. 이 방법을 2003년 SOHO/MDI의 태양 가시광 영상에 적용하여 구한 흑점군의 내부 흑점수와 면적은 NOAA에서 산출한 값들과 각각 90%, 99%의 좋은 상관관계를 가졌다. 우리는 이 연구를 통해 흑점군의 형태학적인 특성과 더불어 예보에 직접적으로 활용할 수 있는 방법을 논의하고자 한다.

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