Faster approximation algorithms for the rectilinear steiner tree problem

Abstract

The classical Steiner Tree Problem requires a shortest tree spanning a given vertex subset within a graph G=(V, E). An important variant is the Steiner tree problem in rectilinear metric. Only recently two algorithms were found which achieve better approximations than the ‘traditional’ one with a factor of 3/2. These algorithms with an approximation ratio of 11/8 are quite slow and run in time O(n3) and O(n5/2). A new simple implementation reduces the time to O(n3/2). As our main result we present efficient parameterized algorithms which reach a performance ratio of 11/8+ε for any ε>0 in time O(n-log2n), and a ratio of 11/8+log log n log n in time O(n-log3n).