C. W. Duin and A. Volgenant. Some generalizations of the Steiner problem in graphs. Networks, 17(2):353--364, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Steiner tree problem and is called the Single Point Weighted Steiner Tree problem. The author proves NP hardness of the problem, presents integer linear programming formulations and uses Lagrangean relaxation and heuristics to compute lower and upper bounds for these formulations, respectively. In [5], Duin and Volgenant relate the node weighted (and thus also the prize collecting) variant to the classical Steiner tree problem. They adapt reduction techniques and show how the rooted prize collecting Steiner tree problem can be transformed into the directed version of the classical Steiner tree ....

C.W. Duin and A. Volgenant. Some generalizations of the Steiner problem in graphs. Networks, 17(2):353 364, 1987.

....[13] Hence much of the work mentioned above focuses on approximation algorithms for these problems. However, in applications that arise in real world situations, it is often the case that the network design problem involves the minimization of more than one of these cost measures simultaneously [9, 16]. In this paper, we concentrate on two objectives: i) the degree of the network and (ii) the total cost of the network. Typically, our goal will be to find networks of minimum cost subject to degree constraints. For example, consider the following problem: Given an undirected graph ....

....for points in the plane. They also presented an approximation algorithm with a performance guarantee of 5 3 for point sets in higher dimensions when . Iwainsky et al. 16] formulated a version of the minimum cost Steiner problem with an additional cost based on node degrees. Duin and Volgenant [9] formulated the degree bounded Steiner tree problem motivated by practical considerations. In other related work, Fischer [11] considered the problem of finding a MST of minimum possible maximum degree in a weighted undirected graph. He showed that the techniques of Furer and Raghavachari [12] can ....

C. W. Duin and A. Volgenant, "Some Generalizations of the Steiner problem in Graphs," Networks, Vol. 17, pp. 353--364, 1987.

....[13] Hence much of the work mentioned above focuses on approximation algorithms for these problems. However, in applications that arise in real world situations, it is often the case that the network design problem involves the minimization of more than one of these cost measures simultaneously [9, 16]. In this paper, we concentrate on two objectives: i) the degree of the network and (ii) the total cost of the network. Typically, our goal will be to find networks of minimum cost subject to degree constraints. For example, consider the following problem: Given an undirected graph G = V; E) ....

....points in the plane. They also presented an approximation algorithm with a performance guarantee of 5 3 for point sets in higher dimensions when 4 d = 3. Iwainsky et al. 16] formulated a version of the minimum cost Steiner problem with an additional cost based on node degrees. Duin and Volgenant [9] formulated the degree bounded Steiner tree problem motivated by practical considerations. In other related work, Fischer [11] considered the problem of finding a MST of minimum possible maximum degree in a weighted undirected graph. He showed that the techniques of Furer and Raghavachari [12] can ....

C. W. Duin and A. Volgenant, "Some Generalizations of the Steiner problem in Graphs," Networks, Vol. 17, pp. 353--364, 1987.

....The solution output is approximate in terms of both the number of median nodes used and the sum of the distances from each vertex to the nearest median. Iwainsky et al. 75] formulated a version of the minimum cost Steiner problem with an additional cost based on node degrees. Duin and Volgenant [36], motivated by practical considerations, formulated the degree bounded Steiner tree problem. Other researchers have addresses multi objective approximation algorithms for problems arising in areas other than network design. Agrawal, Klein and Ravi [89] provided an approximation algorithm for ....

C. W. Duin, an A. Volgenant, "Some generalizations of the Steiner problem in graphs," Networks, 17, pp. 353-364, (1987).

....at most a constant times that of the MST such that the distance in this tree from the root is at most a constant times the distance in the input graph. Iwainsky et al. 16] formulated a version of the minimum cost Steiner problem with an additional cost based on node degrees. Duin and Volgenant [6] formulate the degree bounded Steiner tree problem motivated by practical considerations. 2.2 Minimizing one of the cost measures Much work has been done on approximating each of the cost measures that we simultaneously minimize. A series of recent results have addressed the problem of ....

C. W. Duin, an A. Volgenant, "Some generalizations of the Steiner problem in graphs," Networks, 17, pp. 353-364, (1987).

....k, the goal is to find a forest of minimum cost containing at most q trees spanning all the terminals. When m = 1, we have the classical Steiner tree problem where a single tree of minimum cost spanning all the terminals is required. The Steiner forest problem was introduced by Duin and Volgenant [4] motivated by the following application. A tree in the forest spanning a subset of the terminals represents establishing a service for the terminals in the tree. The cost of the tree may be taken to be the cost of providing the service. The q Steiner forest problem corresponds to minimizing the ....

C. W. Duin, and A. Volgenant, "Some generalizations of the Steiner problem in graphs," Networks, 17, pp. 353-364, (1987).

.... techniques proposed for optimizing communications subnetwork topologies and network provisioning [15] 52] 42] 35] minimum area routing in VLSI circuits [16] minimum cost pipeline interconnections for subnetworks of oil wells [44] and minimum cost interconnections for cable TV subnetworks [20]. The principal theoretical results presented here are: 1. A polynomial time greedy algorithm for constructing an approximation to the minimal k point graph and its edge weight function is presented which is a direct generalization of the algorithm of Ravi, Sundaram, Marathe, Rosenkrantz and Ravi ....

C. W. Duln and A. Volgenant, \Some generalizations of the Steiner problem in graphs," Networks, vol. 17, pp. 353-364, 1987.

....[1] Maculan [32] Lucena [31] Wong [48] and Chopra, Gorres, and Rao [7] Exact algorithms for the SPG can benefit from preprocessing the graph so that the size of the problem to solve is reduced. Reduction techniques are discussed in Beasley [3] Balakrishnan and Patel [2] Duin and Volgenant [13, 14], Voss [44, 45] Iwainsky et al. 24] Chopra, Gorres, and Rao [7] Khoury and Pardalos [27] and Duin [11, 12] Many heuristics have been proposed to find approximate solutions for the SPG. For example, in Aneja [1] a greedy variation of a set covering algorithm is presented, and an MST based ....

C.W. Duin and A. Volgenant. Some generalizations of the Steiner problem in graphs. Networks, 17:353--364, 1987.

....[1] Maculan [32] Lucena [31] Wong [48] and Chopra, Gorres, and Rao [7] Exact algorithms for the SPG can benefit from preprocessing the graph so that the size of the problem to solve is reduced. Reduction techniques are discussed in Beasley [3] Balakrishnan and Patel [2] Duin and Volgenant [13, 14], Voss [44, 45] Iwainsky et al. 24] Chopra, Gorres, and Rao [7] Khoury and Pardalos [27] and Duin [11, 12] Many heuristics have been proposed to find approximate solutions for the SPG. For example, in Aneja [1] a greedy variation of a set covering algorithm is presented, and an MST based ....

C.W. Duin and A. Volgenant. Some generalizations of the Steiner problem in graphs. Networks, 17:353--364, 1987.

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C. W. Duin and A. Volgenant. Some generalizations of the Steiner problem in graphs. Networks, 17(2):353--364, 1987.

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C. W. Duin and A. Volgenant. Some generalizations of the Steiner problem in graphs. Networks, 17(2):353--364, 1987.

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C. W. Duin and A. Volgenant. Some generalizations of the Steiner problem in graphs. Networks, 17(2):353--364, 1987.

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C. W. Duin and A. Volgenant. Some generalizations of the Steiner problem in graphs. Networks, 17(2):353--364, 1987.

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