• 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.

• 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 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.

• Journal of Communications and Networks
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• v.4 no.3
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• pp.246-255
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• 2002

Constrained minimum Steiner tree (CMST) problem is a key issue in multicast routing with quality of service (QoS) support. Bounded shortest path algorithm (BSMA) has been recognized as one of the best algorithms for the CMST problem due to its excellent cost performance. This algorithm starts with a minimumdelay tree, and then iteratively uses a
-shortest-path (KSP) algorithm to search for a better path to replace a “superedge” in the existing tree, and consequently reduces the cost of the tree. The major drawback of BSMA is its high time complexity because of the use of the KSP algorithm. For this reason, we investigate in this paper the possibility of more efficient implementations of BSMA by using different methods to locate the target path for replacing a superedge. Our experimental results indicate that our methods can significantly reduce the time complexity of BSMA without deteriorating the cost performance.

• 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.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.7_8
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• pp.387-396
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• 2003

This paper provides an approximation algorithm for STP-MSP(Steiner Tree Problem with minimum number of Steiner Points).Because it seems to be impossible to have a PTAS(Polynomial Time Approximation Schemes), which gives the near optimal solutions, for the problem, the algorithm of this paper is an alternative that has the approximation ratio 2 with $n^{O(1)}$ run time. The importance of this paper is the potential to solve other related unsolved problems. The idea of this paper is to distribute the error allowance over the problem instance so that we may reduce the run time to polynomial bound out of infinitely many cases. There are earlier works[1,2] that show the approximations that have practical run times with the ratio of bigger than 2, but this paper shows the existence of a poly time approximation algorithm with the ratio 2.

• Journal of the Korea Society of Computer and Information
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• v.8 no.3
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• pp.150-155
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• 2003

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. This paper proposes an algorithm that reduces the multicast routing costs using a clustering method. Multicast tree is constructed by minimum-cost Steiner tree. It is important to solve the mnimum-cost Steiner tree problem in the multicast routing problems. Hence, this paper proposes a genetic algorithm for multicast routing problems using clustering method.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.4
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• pp.15-25
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• 2000

In this paper, we introduce a point-to-multipoint minimum cost flow problem with convex and demand splitting. A source node transmits the traffic along the tree that includes members of the point-to-multipoint connection. The traffic is replicated by the nodes only at branch points of the tree. In order to minimize the sum of arc costs, we assume that the traffic demand can be splitted and transmitted to destination nodes along different trees. If arc cost is linear, the problem would be a Steiner tree problem in networks eve though demand splitting is permitted. The problem would be applied in transmitting large volume of traffic from a serve to clients in Internet environments. Optimality conditions of the problem are presented in terms of fair tree routing. The proposed algorithm is a finite terminating algorithm for $\varepsilon$-optimal solution. convergence of the algorithm is obtained under monotonic condition and strict convexity of the cost function. Computational experiences are included.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.3
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• pp.81-89
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• 2000

The real-time multicast problem is to construct a multicast tree starting from a source node and including multiple destination nodes and that has minimum network cost with delay constraints. It is known that to find a tree of the minimum network cost is the Steiner Tree problem which is NP-complete. In this paper, we propose a genetic algorithm to solve the multicast tree with minimum network cost and the delay constraints. The computational results obtained by comparing an existing algorithm. Kompella algorithm, and the proposed algorithm show that our algorithm tends to find lower network cost on the average than Kompella algorithm does.

• Journal of the Korea Society of Computer and Information
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• v.16 no.11
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• pp.153-161
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• 2011

As the problem of GOSST building belongs to NP compete domain, heuristics for the problem ask for immense amount execution time and computations in large scale inputs. In this paper, we propose an efficient mechanism for GOSST construction using space locality PTAS. For 40,000 input nodes with maximum weight 100, the proposed space locality PTAS GOSST with 16 unit areas can reduce about 4.00% of connection cost and 89.26% of execution time less than weighted minimum spanning tree method. Though the proposed method increases 0.03% of connection cost more, but cuts down 96.39% of execution time less than approximate GOSST method (SGOSST) without PTAS. Therefore the proposed space locality PTAS GOSST mechanism can work moderately well to many useful applications where a greate number of weighted inputs should be connected in short time with approximate minimum connection cost.