A new approximation algorithm for the Steiner tree problem with performance ratio 5/3

In this paper we present an RNC approximation algorithm for the Steiner tree problem in graphs with performance ratio 5/3 and RNC approximation algorithms for the Steiner tree problem in networks with performance ratio 5/3 + epsilon for all epsilon > 0. This is achieved by considering a related problem, the minimum spanning tree problem in weighted 3-uniform hypergraphs. For that problem we give a fully polynomial randomized approximation scheme. Our approach also gives rise to conceptually much easier and faster (though randomized) sequential approximation algorithms far the Steiner tree problem than the currently best known algorithms from Karpinski and Zelikovsky which almost match their approximation factor. (C) 2000 Academic Press.