• Proceedings of the Korean Operations and Management Science Society Conference
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• 2008.10a
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• pp.430-434
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• 2008

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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.589-598
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• 2006

The rectilinear Steiner tree problem 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. A hybrid evolutionary algorithm is introduced based upon the Prim algorithm. The Prim algorithm for the fitness evaluation requires heavy calculation time. The fitness value of parents is inherited to their child and the fitness value of child is estimated by the inherited structure of tree. We introduce four alternative evolutionary algorithms, Experiment result shows that the calculation time is reduced to 25% without loosing the solution quality by using the fitness estimation.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.25 no.5
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• pp.34-38
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• 2011

The shorter the electric power line is, the less its cost becomes. In this paper, the Steiner tree is applied to find the shortest path of the electric power line to obtain resultant cost reduction. Up to 18.3[%] of length reduction can be expected compared to conventional method when the lines are connected through the Steiner points, which also can result in appreciable cost reduction.

• Journal of Information Processing Systems
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• v.13 no.1
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• pp.104-113
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• 2017

In this paper, we present an approach to transmit data from the source to the destination through a minimal path (least-cost path) in a computer network of n nodes. The motivation behind our approach is to address the problem of finding a minimal path between the source and destination. From the work we have studied, we found that a Steiner tree with bounded Steiner vertices offers a good solution. A novel algorithm to construct a Steiner tree with vertices and bounded Steiner vertices is proposed in this paper. The algorithm finds a path from each source to each destination at a minimum cost and minimum number of Steiner vertices. We propose both the sequential and parallel versions. We also conducted a comparative study of sequential and parallel versions based on time complexity, which proved that parallel implementation is more efficient than sequential.

• Journal of the Korea Society of Computer and Information
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• v.17 no.7
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• pp.87-95
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• 2012

In this paper, PTAS three-dimensional Steiner minimum tree connecting numerous input nodes rapidly in 3D space is proposed. Steiner minimum tree problem belongs to NP problem domain, and when properly devised heuristic introduces, it is generally superior to other algorithms as minimum spanning tree affiliated with P problem domain. But when the number of input nodes is very large, the problem requires excessive execution time. In this paper, a method using PTAS is proposed to solve the difficulty. In experiments for 70,000 input nodes in 3D space, the tree produced by the proposed 8 space partitioned PTAS method reduced 86.88% execution time, compared with the tree by naive 3D steiner minimum tree method, though increased 0.81% tree length. This affirms the proposed method can work well for applications that many nodes of three dimensions are need to connect swifty, enduring slight increase of tree length.

• Journal of Communications and Networks
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• v.9 no.1
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• pp.84-92
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• 2007

This paper deals with the creation of multicast trees in a differentiated services (DiffServ) domain. Initially, we model the integration problems of multicast & DiffServ and give a general de-scription of our framework for multicast provisioning in DiffServ domains. Within this framework, we introduce a novel heuristic algorithm which calculates the multicast trees efficiently. The multicast tree's format and the bandwidth constraints per service class are modeled. The heuristic is based on the Dijkstra's shortest path algorithm and aims to produce the cheapest possible trees (Steiner tree problem) that conform to the defined model. The produced trees can be considered as DiffServ-customized Steiner trees. Furthermore, we evaluate the algorithm with theoretical and experimental analysis and finally, we present our conclusions.

• Journal of Korea Multimedia Society
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• v.11 no.1
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• pp.44-52
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• 2008

This paper is on the enhancement of our heuristics for Grade Of Services Steiner Minimum Tree (GOSST) problem that can apply to the design of communication networks offering manifold grade of services in multimedia communication area. GOSST problem known as one of NP-Hard problems asks for a network topology meeting the G-Condition with minimum construction cost. In our prior researches, we proposed some heuristics for the problem. In this paper, we suggest a strategy of G-Condition scrutiny sequence to fortify our previous heuristics. In the experiment results, the ameliorated achieves 71.9% economy of execution times, 28.9% of required Steiner points and 1.1% of network construction costs.

• 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.

• 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.

• The Transactions of the Korea Information Processing Society
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• v.3 no.7
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• pp.1707-1718
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• 1996

Given a signal net N=s, 1,...,n to be the set of nodes, with s the source and the remaining nodes sinks, an MRDPT (minimum-cost rectilinear Steiner distance -preserving tree) has the property that the length of every source to sink path is equal to the rectilinear distance between the source and sink. The minimum- cost rectilinear Steiner distance-preserving tree minimizes the total wore length while maintaining minimal source to sink length. Recently, some heuristic algorithms have been proposed for the problem offending the MRDPT. In this paper, we investigate an optimal structure on the MRDPT and present a theoretical breakthrough which shows that the min-cost flow formulation leads to an efficient O(n2logm)2) time algorithm. A more practical extension is also in vestigated along with interesting open problems.