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In the past, several heuristic algorithms were developed for the topological via minimization problem. It was very recently shown to be NP-hard even for the two-layer channel routing case with two-terminal nets only. The authors show that if no local net exists in a channel, this problem is solvable in O(kn/sup 2/) time even for k layers, where n is the number of two-terminal nets. As an extension of this case, they consider the problem for the case of k-layer circular channel routing in which no local net exists and present an O(n/sup 2k+1/) time algorithm.>
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Rim et al. (1989) studied this question.
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