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The generalized minimum spanning tree problem consists of designing a minimum cost tree spanning several clusters.
The nodes that immediately follow the root node in the minimum cost tree constitute the minimum neighborhood of node.
Given a graph whose vertex set is partitioned into clusters, the GMSTP consists of designing a minimum cost tree spanning all clusters.
The design of a DDS network is a special case of the classic Steiner-tree problem of finding the minimum cost tree connecting a set of nodes, using Steiner nodes.
We show that when ∑u∈Vbu+="∑v∈Vbu-, designing a minimum cost tree network is easy and the cost of an optimal tree reservation is within a factor of three of the cost of any reservation.
The minimum cost tree over all such subsets and all possible values of k is returned as the optimal tree.
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(c) Computation of the minimum-cost tree (Steiner tree).
Next, according to the target groups {6, 13, 10}, using the method [31, 32], the minimum-cost tree (Steiner tree) can be computed, which is shown in Figure 5c.
We also present an algorithm for the calculation of the minimum-cost tree, which connects the source with the destinations, taking into account the available bandwidth per service class.
Apart from finding the minimum-cost tree and using metrics on the physical performance of the system, namely the Q-factor, this work investigates different node architecture designs including architectures with active and passive splitters and architectures with different receiver and transmitter designs.
This secure communication path, from the original group manager to the target group manager, can be obtained by computing a minimum cost multicast tree, commonly known as the Steiner tree.
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