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In this paper, the authors study the global routing problem in VLSI design and the multicast routing problem in communication networks. First, they propose new and realistic models for both problems. In the global routing problem in VLSI design, they are given a lattice graph and subsets of the vertex set. The goal is to generate trees spanning these vertices in the subsets to minimize a linear combination of overall wirelength (edge length) and the number of bends of trees with respect to edge capacity constraints. In the multicast routing problem in communication networks, a graph is given to represent the network, together with subsets of the vertex set.
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