On the bidirected cut relaxation for the metric Steiner tree problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
New geometry-inspired relaxations and algorithms for the metric steiner tree problem
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
Steiner Tree Approximation via Iterative Randomized Rounding
Journal of the ACM (JACM)
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Let G = (V, E) be an undirected graph with costs on the edges specified by w : E → R+. A Steiner tree is any tree of G which spans all nodes in a given subset R of V. When V\R is a stable set of G, then (G, R) is called quasi-bipartite. Rajagopalan and Vazirani [SODA'99, 1999, pp. 742-751] introduced the notion of quasi-bipartiteness and showed that the Iterated 1-Steiner heuristic always produces a Steiner tree of total cost at most 3/2 the optimal when (G, R) is quasi-bipartite and w is a metric. In this paper, we give a more direct and much simpler proof of this result. Next, we show how a bit scaling approach yields a polynomial time implementation of the Iterated 1-Steiner heuristic. This gives a 3/2 approximation algorithm for the problem considered by Rajagopalan and Vazirani. (We refer however to the recent and independent developments by Robins and Zelikovsky [SODA'00, 2000] for better bounds and algorithms.) Finally, our bit scaling arguments are not standard and we are the first to adapt bit scaling techniques to the design of approximation algorithms.