• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.10a
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• pp.27-37
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• 2005

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 evolution strategy on RSTP based upon the Prim algorithm was presented. The computational results show that the evolution strategy is better than the previously proposed other heuristic. The average reduction rate of solutions from the evolution strategy is about 11%, which is almost similar to that of optimal solutions.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.1056-1064
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• 2003

The Euclidean steiner tree problem (ESTP) is to find a minimum-length euclidean interconnection of a set of points 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, and the ESTP is NP-complete. The ESTP has received a lot of attention in the literature, and heuristic and optimal algorithms have been proposed. In real field, heuristic algorithms for ESTP are popular. A key performance measure of the algorithm for the ESTP is the reduction rate that is achieved by the difference between the objective value of the ESTP and that of the MST without steiner points. In recent survey for ESTP, the best heuristic algorithm showed around $3.14\%$ reduction in the performance measure. We present a evolution programming (EP) for ESTP based upon the Prim algorithm for the MST problem. The computational results show that the EP can generate better results than already known heuristic algorithms.

• The KIPS Transactions:PartA
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• v.17A no.5
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• pp.213-220
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• 2010

In this paper, a mechanism connecting all input edges with minimum length through Steiner tree is proposed. Edges are convertible into communication lines, roads, railroads or trace of moving object. Proposed mechanism could be applied to connect these edges with minimum cost. In our experiments where input edge number and maximum connections per edge are used as input parameters, our mechanism made connection length decrease average 6.8%, while building time for a connecting solution increase average 192.0% comparing with the method using minimum spanning tree. The result shows our mechanism might be well applied to the applications where connecting cost is more important than building time for a connecting solution.

• Management Science and Financial Engineering
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• v.12 no.2
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• pp.63-69
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• 2006

To generate a multicast routing tree guaranteeing the quality of service (QoS), we consider the hop constrained Steiner tree problem and propose a new mathematical formulation for it, which contains fewer constraints than a known formulation. An efficient procedure is also proposed to solve the problem. Preliminary tests show that the procedure reduces the computing time significantly.

• Korean Management Science Review
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• v.26 no.1
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• pp.65-76
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• 2009

The undirected Steiner tree problem in graphs is known to be NP-hard. The objective of this problem is to find a shortest tree containing a subset of nodes, called 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 edges which do not contribute to make an optimal solution. In the second step, a max-min ant colony optimization combined with Prim's algorithm is developed to solve the reduced problem. The proposed algorithm is tested in the sets of standard test problems. The results show that the algorithm efficiently presents very correct solutions to the benchmark problems.

• The Transactions of the Korea Information Processing Society
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• v.5 no.3
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• pp.671-680
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• 1998

Network services, such as teleconferencing, remote diagnostics and education, and CSCW require multicasting. Multicast routing methods can be divided into two categories. One is the shortest path tree method and the other is the minimal Steiner tree method. The latter has an advantage over the former in that only one Steiner tree is needed for a group. However, finding a minimal Steiner tree is an NP-complete problem and it is necessary to find an efficient heuristic algorithm. In this paper, we present an evolutionary optimization method for finding minimal Steiner trees without sacrificing too much computational efforts. In particular, we describe a tree-based genetic encoding scheme which is in sharp constast with binary string representations usually adopted in convetional genetic algorithms. Experiments have been performed to show that the presented method can find optimal Steiner trees for given vetwork configurations. Comparitivie studies have shown that the evolutionary method finds on average a better solution than other conventional heustric algorithms.

• Journal of the Korea Society of Computer and Information
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• v.9 no.3
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• pp.189-194
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• 2004

This paper proposes a Simulated Annealing(SA) algorithm for cluster-based Multicast Routing problems. Multicasting, the transmission of data to a group, can be solved from constructing multicast tree, that is. the whole network is partitioned to some clusters and the clusters are constructed by multicast tree. Multicast tree can be constructed by minimum-cost Steiner tree. In this paper, an SA algorithm is used in the minimum-cost Steiner tree. Especially, in SA, the cooling schedule is an important factor for the algorithm. Hence, in this paper, a cooling schedule is proposed for SA for multicast routing problems and analyzed the simulation results.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.3
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• pp.17-33
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• 2000

We consider the Steiner tree packing problem. For a given undirected graph G =(V, E) with positive integer capacities and non-negative weights on its edges, and a list of node sets(nets), the problem is to find a connection of nets which satisfies the edge capacity limits and minimizes the total weights. We focus on the switchbox routing problem in knock-knee model and formulate this problem as an integer programming using Steiner tree variables. The model contains exponential number of variables, but the problem can be solved using a polynomial time column generation procedure. We test the algorithm on some standard test instances and compare the performances with the results using cutting plane approach. Computational results show that our algorithm is competitive to the cutting plane algorithm presented by Grotschel et al. and can be used to solve practically sized problems.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.3
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• pp.61-72
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• 2002

In this paper, we propose two timing-driven routing algorithms for single-source net and multi-source net as applications of 1-Steiner heuristic algorithm. Using the method of substituting the cost of 1-Steiner heuristic algorithms with interconnection delay, our routing algorithms can route both single-source net and multi-source net which have all critical source-terminal pairs or one critical pair efficiently Our single-source net routing algorithm reduced the average maximum interconnection delay by up to 2.1% as compared with previous single-source routing algorithm, SERT, and 10.6% as compared with SERT-C. and Our multi-source net routing algorithm increased the average maximum interconnection delay by up to 2.7% as compared with MCMD A-tree, but outperforms it by up to average 1.4% when the signal net has only subset of critical node pairs.

• Korean Management Science Review
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• v.28 no.1
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• pp.1-10
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• 2011

One of the fundamental roles of web object navigation is to support what the user wants precisely and efficiently from the enormous web database to the web browser. As long as the web search results are a set of individual lists, it is all right to display each and every web result for the web browser to display a web object one by one. However, in case the search results are a collection of multiple interrelated web objects, then there is a need to represent for a new mechanism for linked web objects at a time. We define a unit of web objects derived from a Steiner tree where the web objects include a set of specific keywords calculated by the weight from which the solutions are extracted. Even if a web object does not include all the keywords, then the related hypertext linked web objects are derived and displayed onto the mobile web browser with meta data in one shot. In this paper, it is applied for the mobile browser that the web contents can dynamically be displayed with Steiner trees until each renewal of the navigation request may be issued. In this paper, a new synchronized mobile browsing method is developed so that the navigating time can drastically be reduced and the web navigating efficiency can be dramatically enhanced without sacrificing memory consumption.