Abstract
The Steiner problem on networks asks for a shortest subgraph spanning a given subset of distinguished vertices. We give a 4 3 -approximation algorithm for the special case in which the underlying network is complete and all edge lengths are either 1 or 2. We also relate the Steiner problem to a complexity class recently defined by Papadimitriou and Yannakakis by showing that this special case is MAX SNP-hard, which may be evidence that the Steiner problem on networks has no polynomial-time approximation scheme.
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