A Polynomial-Time Approximation Scheme for Euclidean Steiner Forest

We give a randomized O(n
²
log n)-time approximation scheme for the Steiner forest problem in the Euclidean plane. For every fixed epsi > 0 and given any n pairs of terminals in the plane, our scheme finds a (1 + epsi)- approximation to the minimum-length forest that connects every pair of terminals.