On the Steiner Tree -Approximation for Quasi-Bipartite Graphs Romeo Rizzi November 1999

### Abstract:

Let be an undirected simple graph and be a non-negative weighting of the edges of . Assume is partitioned as . A Steiner tree is any tree of such that every node in is incident with at least one edge of . The metric Steiner tree problem asks for a Steiner tree of minimum weight, given that is a metric. When is a stable set of , then is called quasi-bipartite. In a SODA '99 paper, Rajagopalan and Vazirani introduced the notion of quasi-bipartiteness and gave a approximation algorithm for the metric Steiner tree problem, when 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

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