A polynomial-time approximation scheme for Euclidean Steiner forest

Abstract: We give a randomized O(n polylog n)-time approximation scheme for the Steiner forest problem in the Euclidean plane. For every fixed eps > 0 and given n terminals in the plane with connection requests between some pairs of terminals, our scheme finds a (1 + eps)-approximation to the minimum-length forest that connects every requested pair of terminals.