Abstract
In a recent paper [5], we addressed the problem of finding a minimum-cost spanning tree T for a given undirected graph G=(V,E) with maximum node-degree at most a given parameter B>1. We developed an algorithm based on Lagrangean relaxation that uses a repeated application of Kruskal’s MST algorithm interleaved with a combinatorial update of approximate Lagrangean node-multipliers maintained by the algorithm.
In this paper, we show how to extend this algorithm to the case of Steiner trees where we use a primal-dual approximation algorithm due to Agrawal, Klein, and Ravi [1] in place of Kruskal’s minimum-cost spanning tree algorithm. The algorithm computes a Steiner tree of maximum degree O(B + log n) and total cost that is within a constant factor of that of a minimum-cost Steiner tree whose maximum degree is bounded by B. However, the running time is quasi-polynomial.
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References
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Könemann, J., Ravi, R. (2003). Quasi-polynomial Time Approximation Algorithm for Low-Degree Minimum-Cost Steiner Trees. In: Pandya, P.K., Radhakrishnan, J. (eds) FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2003. Lecture Notes in Computer Science, vol 2914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24597-1_25
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DOI: https://doi.org/10.1007/978-3-540-24597-1_25
Publisher Name: Springer, Berlin, Heidelberg
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