-Approximation for Quasi-Bipartite Graphs

Let G = (V, E) be an undirected simple graph and w : E 7→ IR+ be a non-negative weighting of the edges of G. Assume V is partitioned as R ∪ X . A Steiner tree is any tree T of G such that every node in R is incident with at least one edge of T . The metric Steiner tree problem asks for a Steiner tree of minimum weight, given that w is a metric. When X is a stable set of G, then (G, R, X) is called quasibipartite. In [1], Rajagopalan and Vazirani introduced the notion of quasi-bipartiteness and gave a (32 + ) approximation algorithm for the metric Steiner tree problem, when (G, R, X) is quasi-bipartite. In this paper, we simplify and strengthen the result of Rajagopalan and Vazirani. We also show how classical bit scaling techniques can be adapted to the design of approximation algorithms.