• Title, Summary, Keyword: Steiner tree

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Design of Minimal Postal Transportation Path using Steiner Tree (Steiner Tree 이론을 이용한 최적 우편물 운송망 구축)

  • Lyu, Woong-Gyu;Lee, Sang-Joong
    • Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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    • pp.183-186
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    • 2007
  • Faster, safer and cheaper mailing of the postal matter is essential for surviving in the competitive market of home-delivery service. The Steiner tree connects points minimally in geometrical way and has been used in the distribution system optimization and optimal routing of the transmission lines of the electric power system. This paper proposes a method to select the optimal location of mail distribution center that minimally connect the local mail center of some major cities using the Steiner tree theorem.

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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.

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.

Optimal Location of Mail Distribution Center using Steiner Tree (Steiner Tree 이론을 이용한 우편물 교환센터인 최적 워치선정)

  • Yang, Seong-Deog;Lyu, Woong-Gyu;Lee, Sang-Joong
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.22 no.9
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    • pp.82-87
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    • 2008
  • Faster, safer and cheaper mailing of the postal matter is essential for surviving in the competitive market of home-delivery service. In the past, the domestic delivery business has been nu by only a few number of companies. But more and more number of companies including medium size ones are participating in the business, and the competition is getting severe. This paper proposes a method to select the optimal location of mail distribution centers that minimally connect the local mail centers of some major cities in Korea using the Steiner Tree theory, which is about connecting a finite number of points with a minimal length of paths and has been used in the distribution system optimization and optimal routing of the transmission lines of the electric power system. By using Steiner Tree theory in finding the best location of the postal delivery hub, we may expect the reduction of transportation cost and the increase of profit, resulting in acquiring the superior position in the competitive delivery business. It is expected that we may use the Steiner Tree theory in finding the best location of the electric power substation for the nott higher EHV(extreme high voltage) transmission network.

A Comparison of Group Steiner Tree Formulations (그룹-스타이너-트리 문제의 수학적 모형에 대한 연구)

  • Myung, Young-Soo
    • Journal of Korean Institute of Industrial Engineers
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    • v.37 no.3
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    • pp.191-197
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    • 2011
  • The group Steiner tree problem is a generalization of the Steiner tree problem that is defined as follows. Given a weighted graph with a family of subsets of nodes, called groups, the problem is to find a minimum weighted tree that contains at least one node in each group. We present some existing and some new formulations for the problem and compare the relaxations of such formulations.

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.

Design and Implementation of a Genetic Algorithm for Global Routing (글로벌 라우팅 유전자 알고리즘의 설계와 구현)

  • 송호정;송기용
    • Journal of the Institute of Convergence Signal Processing
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    • v.3 no.2
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    • pp.89-95
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    • 2002
  • Global routing is to assign each net to routing regions to accomplish the required interconnections. The most popular algorithms for global routing inlcude maze routing algorithm, line-probe algorithm, shortest path based algorithm, and Steiner tree based algorithm. In this paper we propose weighted network heuristic(WNH) as a minimal Steiner tree search method in a routing graph and a genetic algorithm based on WNH for the global routing. We compare the genetic algorithm(GA) with simulated annealing(SA) by analyzing the results of each implementation.

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A Proposal of Heuristic Using Zigzag Steiner Point Locating Strategy for GOSST Problem (GOSST 문제 해결을 위한 지그재그 스타이너 포인트 배치 방법을 이용한 휴리스틱의 제안)

  • Kim, In-Bum;Kim, Chae-Kak
    • The KIPS Transactions:PartA
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    • v.14A no.5
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    • pp.317-326
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    • 2007
  • We propose more enhanced heuristic for the GOSST(Grade of Services Steiner Minimum Tree) problem in this paper. GOSST problem is a variation of Steiner Tree problem and to find a network topology satisfying the G-Condition with minimum network construction cost. GOSST problem is known as one of NP-Hard or NP-Complete problems. In previous our research, we proposed a heuristic employing Direct Steiner Point Locating strategy with Distance Preferring MST building strategy. In this paper, we propose new Steiner point locating strategy, Zigzag Steiner point Locating strategy. Through the results of out experiments, we can assert this strategy is better than our previous works. The Distance Zigzag GOSST method which hires the Distance Preferring MST building strategy and Zigzag Steiner point Locating strategy defrays the least network construction cost and brings 31.5% cost saving by comparison to G-MST, the experimental control and 2.2% enhancement by comparison to the Distance Direct GOSST method, the best GOSST method in our previous research.

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.

A Nodes Set Based Hybrid Evolutionary Strategy on the Rectilinear Steiner Tree Problem (점집합을 개체로 이용한 직각거리 스타이너 나무 문제의 하이브리드 진화 전략에 관한 연구)

  • Yang Byoung-Hak
    • Korean Management Science Review
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    • v.23 no.1
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    • pp.75-85
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    • 2006
  • The rectilinear Steiner tree problem (RSTP) is to find a minimum-length rectilinear interconnection of a set of terminals in the plane. It is well known that the solution to this problem will be the minimal spanning tree(MST) on some set Steiner points. The RSTP is known to be NP-complete. The RSTP has received a lot of attention in the literature and heuristic and optimal algorithms have been proposed. A key performance measure of the algorithm for the RSTP is the reduction rate that is achieved by the difference between the objective value of the RSTP and that of the MST without Steiner points. A hybrid evolutionary strategy on RSTP based upon nodes set is presented. The computational results show that the hybrid evolutionary strategy is better than the previously proposed other heuristic. The average reduction rate of solutions from the evolutionary strategy is about 11.14%, which is almost similar to that of optimal solutions.