• Title/Summary/Keyword: minimum spanning trees

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Proposal of Minimum Spanning Tree Algorithm using 2-Edges Connected Grap (2-간선 연결 그래프를 사용한 최소신장트리 알고리즘 제안)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.14 no.4
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    • pp.233-241
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    • 2014
  • This paper suggests a fast minimum spanning tree algorithm which simplify the original graph to 2-edge connected graph, and using the cycling property. Borůvka algorithm firstly gets the partial spanning tree using cycle property for one-edge connected graph that selects the only one minimum weighted edge (e) per vertex (v). Additionally, that selects minimum weighted edge between partial spanning trees using cut property. Kruskal algorithm uses cut property for ascending ordered of all edges. Reverse-delete algorithm uses cycle property for descending ordered of all edges. Borůvka and Kruskal algorithms always perform |e| times for all edges. The proposed algorithm obtains 2-edge connected graph that selects 2 minimum weighted edges for each vertex firstly. Secondly, we use cycle property for 2-edges connected graph, and stop the algorithm until |e|=|v|-1 For actual 10 benchmark data, The proposed algorithm can be get the minimum spanning trees. Also, this algorithm reduces 60% of the trial number than Borůvka, Kruskal and Reverse-delete algorithms.

A Design of Efficient Cluster Sensor Network Using Approximate Steiner Minimum Tree (근사 최소 스타이너 트리를 이용한 효율적인 클러스터 센서 네트워크의 구성)

  • Kim, In-Bum
    • The KIPS Transactions:PartA
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    • v.17A no.2
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    • pp.103-112
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    • 2010
  • Cluster sensor network is a sensor network where input nodes crowd densely around some nuclei. Steiner minimum tree is a tree connecting all input nodes with introducing some additional nodes called Steiner points. This paper proposes a mechanism for efficient construction of a cluster sensor network connecting all sensor nodes and base stations using connections between nodes in each belonged cluster and between every cluster, and using repetitive constructions of approximate Steiner minimum trees. In experiments, while taking 1170.5% percentages more time to build cluster sensor network than the method of Euclidian minimum spanning tree, the proposed mechanism whose time complexity is O($N^2$) could spend only 20.3 percentages more time for building 0.1% added length network in comparison with the method of Euclidian minimum spanning tree. The mechanism could curtail the built trees' average length by maximum 3.7 percentages and by average 1.9 percentages, compared with the average length of trees built by Euclidian minimum spanning tree method.

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.

Approximation Algorithms for a Minimum-Diameter Spanning Tree (최소 지름 신장 트리를 구하는 근사 알고리즘)

  • 신찬수;박상민
    • 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.

Two Phase Heuristic Algorithm for Mean Delay constrained Capacitated Minimum Spanning Tree Problem (평균 지연 시간과 트래픽 용량이 제한되는 스패닝 트리 문제의 2단계 휴리스틱 알고리즘)

  • Lee, Yong-Jin
    • The KIPS Transactions:PartC
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    • v.10C no.3
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    • pp.367-376
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    • 2003
  • This study deals with the DCMST (Delay constrained Capacitated Minimum Spanning Tree) problem applied in the topological design of local networks or finding several communication paths from root node. While the traditional CMST problem has only the traffic capacity constraint served by a port of root node, the DCMST problem has the additional mean delay constraint of network. The DCMST problem consists of finding a set of spanning trees to link end-nodes to the root node satisfying the traffic requirements at end-nodes and the required mean delay of network. The objective function of problem is to minimize the total link cost. This paper presents two-phased heuristic algorithm, which consists of node exchange, and node shift algorithm based on the trade-off criterions, and mean delay algorithm. Actual computational experience and performance analysis show that the proposed algorithm can produce better solution than the existing algorithm for the CMST problem to consider the mean delay constraint in terms of cost.

Efficient Construction of Large Scale Steiner Tree using Polynomial-Time Approximation Scheme (PTAS를 이용한 대형 스타이너 트리의 효과적인 구성)

  • Kim, In-Bum
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.47 no.5
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    • pp.25-34
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    • 2010
  • By introducing additional nodes called Steiner points, the problem of Steiner Minimum Tree whose length can be shorter than Minimum Spanning Tree and which connects all input terminal nodes belongs to Non-Polynomial Complete domain. Though diverse heuristic methods can be applied to the problem, most of them may meet serious pains in computing and waiting for a solution of the problem with numerous input nodes. For numerous input nodes, an efficient PTAS approximation method producing candidate unit steiner trees with portals in most bottom layer, merging them hierarchically to construct their parent steiner trees in upper layer and building swiftly final approximation Steiner tree in most top layer is suggested in this paper. The experiment with 16,000 input nodes and designed 16 unit areas in most bottom layer shows 85.4% execution time improvement in serial processing and 98.9% in parallel processing comparing with pure Steiner heuristic method, though 0.24% overhead of tree length. Therefore, the suggested PTAS Steiner tree method can have a wide range applications to build a large scale approximation Steiner tree quickly.

On Minimum Cost Multicast Routing Based on Cost Prediction

  • Kim, Moon-Seong;Mutka, Matt W.;Hwang, Dae-Jun;Choo, Hyun-Seung
    • Journal of Communications and Networks
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    • v.11 no.5
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    • pp.500-508
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    • 2009
  • We have designed an algorithm for a problem in multicast communication. The problem is to construct a multicast tree while minimizing its cost, which is known to be NP-complete. Our algorithm, which employs new concepts defined as potential cost and spanning cost, generates a multicast tree more efficiently than the well-known heuristic called Takahashi and Matsuyama (TM) [1] in terms of tree cost. The time complexity of our algorithm is O($kn^2$) for an n-node network with k members in the multicast group and is comparable to the TM. Our empirical performance evaluation comparing the proposed algorithm with TM shows that the enhancement is up to 1.25%~4.23% for each best case.

Efficient Allocation and Connection of Concentrators and Repeaters Using Approximate Steiner Minimum Tree in Automatic Meter Reading System (원격 검침 시스템에서 근사 최소 스타이너 트리를 이용한 집중기 및 중계기의 효율적인 배치와 연결)

  • Kim, Chae-Kak;Kim, In-Bum;Kim, Soo-In
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.34 no.10B
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    • pp.994-1003
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    • 2009
  • For Automatic Meter Reading System, good topology of check machines, concentrators, and repeaters in client field is important. Steiner Minimum Tree is a minimum cost tree connecting all given nodes with introducing Steiner points. In this paper, an efficient mechanism allocating and connecting check machines, concentrators and repeaters which are essential elements in automatic meter reading system is proposed, which conducts repeated applications of building approximate Minimum Steiner Trees. In the mechanism, input nodes and Steiner points might correspond to check machine, concentrators or repeaters and edges might do to the connections between them. Therefore, through suitable conversions and processes of them, an efficient network for automatic meter reading system with both wired and wireless communication techniques could be constructed. In our experiment, for 1000 input nodes and 200 max connections per node, the proposed mechanism shortened the length of produced network by 19.1% comparing with the length of Minimum Spanning Tree built by Prim's algorithm.

(A Centroid-based Backbone Core Tree Generation Algorithm for IP Multicasting) (IP 멀티캐스팅을 위한 센트로이드 기반의 백본코아트리 생성 알고리즘)

  • 서현곤;김기형
    • Journal of KIISE:Information Networking
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    • v.30 no.3
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    • pp.424-436
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    • 2003
  • In this paper, we propose the Centroid-based Backbone Core Tree(CBCT) generation algorithm for the shared tree-based IP multicasting. The proposed algorithm is based on the Core Based Tree(CBT) protocol. Despite the advantages over the source-based trees in terms of scalability, the CBT protocol still has the following limitations; first, the optimal core router selection is very difficult, and second, the multicast traffic is concentrated near a core router. The Backbone Core Tree(BCT) protocol, as an extension of the CBT protocol has been proposed to overcome these limitations of the CBT Instead of selecting a specific core router for each multicast group, the BCT protocol forms a backbone network of candidate core routers which cooperate with one another to make multicast trees. However, the BCT protocol has not mentioned the way of selecting candidate core routers and how to connect them. The proposed CBCT generation algorithm employs the concepts of the minimum spanning tree and the centroid. For the performance evaluation of the proposed algorithm, we showed the performance comparison results for both of the CBT and CBCT protocols.

Densitometric features of cell nuclei for grading bladder carcinoma (세포핵 조밀도에 의한 방광암의 진행 단계)

  • Choi, Heung-Kook;Bengtsson, Ewert
    • Proceedings of the KOSOMBE Conference
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    • v.1996 no.11
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    • pp.357-362
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    • 1996
  • A way of quantitatively describing the tissue architecture we have investigated when developing a computer program for malignancy grading of transitional cell bladder carcinoma. The minimum spanning trees, MST was created by connecting the center points of the nuclei in the tissue section image. These nuclei were found by thresholding the image at an automatically determined threshold followed by a connected component labeling and a watershed algorithm for separation of overlapping nuclei. Clusters were defined in the MST by thresholding the edge lengths. For these clusters geometric and densitometric features were measures. These features were compared by multivariate statistical methods to the subjective grading by the pathologists and the resulting correspondence was 85% on a material of 40 samples.

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