On the Steiner Tree 3/2-Approximation for Quasi-Bipartite Graphs

Abstract

Let G = (V,E) be an undirected simple graph and w : E -> R+ be
a non-negative weighting of the edges of G. Assume V is partitioned
as R union 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 quasi-bipartite.
In [1], Rajagopalan and Vazirani introduced the notion of
quasi-bipartiteness and gave a ( 3/2 + epsilon) 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.

Key words: Steiner tree, local search, approximation algorithm, bit scaling.