<p>Let G = (V,E) be an undirected simple graph and w : E -> R+ be<br />a non-negative weighting of the edges of G. Assume V is partitioned<br />as R union X. A Steiner tree is any tree T of G such that every node<br />in R is incident with at least one edge of T. The metric Steiner tree<br />problem asks for a Steiner tree of minimum weight, given that w is a<br />metric. When X is a stable set of G, then (G,R,X) is called quasi-bipartite.<br /> In [1], Rajagopalan and Vazirani introduced the notion of<br />quasi-bipartiteness and gave a ( 3/2 + epsilon) approximation algorithm<br /> for the metric Steiner tree problem, when (G,R,X) is quasi-bipartite. In this<br />paper, we simplify and strengthen the result of Rajagopalan and Vazirani.<br />We also show how classical bit scaling techniques can be adapted<br />to the design of approximation algorithms.</p><p>Key words: Steiner tree, local search, approximation algorithm, bit scaling.</p><p> </p>
Local Search for Weighted Tree Augmentation and Steiner Tree
