• 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.

• 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.

• 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.

• 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.

• 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.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.

• The Transactions of the Korea Information Processing Society
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• v.5 no.4
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• pp.1033-1043
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• 1998

In this paper, we present an improved multicasting path assignment algorithm based on the minimum cost spanning tree. In the method presented in this paper, a multicasting path is assigned preferentially when a node to be received is found among the next degree nodes of the searching node in the multicasting path assignment of the constrained steiner tree (CST). If nodes of the legacy group exist between nodes of the new group, a new path among the nodes of new group is assigned as long as the nodes may be excluded from the new multicasting path assignment taking into consideration characteristics of nodes in the legacy group. In assigning the multicasting path additionally, where the source and destination nodes which can be set for the new multicasting path exist in the domain of identical network (local area network) and conditions for degree constraint are satisfied, a method of producing and assigning a new multicasting path is used. The results of comparison of CST with MCSTOP, MCSTOp algorithm enhanced performance capabilities about the communication cost, the propagation delay, and the computation time for the multicasting assignment paths more than CST algorithm. Further to this, research activities need study for the application of the international standard protocol(multicasting path assignment technology in the multipoint communication service (MCS) of the ITU-T T.120).

• 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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.402-408
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• 2002

Multicast technology allows the transmission of data from one source node to a selected group of destination nodes. Multicast routes typically use trees, called multicast routing trees, to minimize resource usage such as cost and bandwidth by sharing links. Moreover, the quality of service (QoS) is satisfied by distributing data along a path haying no more than a given number of arcs between the root node of a session and a terminal node of it in the routing tree. Thus, a multicast routing tree for a session can be represented as a hop constrained Steiner tree. In this paper, we consider the hop-constrained multicast route packing problem with bandwidth reservation. Given a set of multicast sessions, each of which has a hop limit constraint and a required bandwidth, the problem is to determine a set of multicast routing trees in an arc-capacitated network to minimize cost. We propose an integer programming formulation of the problem and an algorithm to solve it. An efficient column generation technique to solve the linear programming relaxation is proposed, and a modified cover inequality is used to strengthen the integer programming formulation.