Abstract
The Steiner tree problem in unweighted graphs requires to find a minimum size connected subgraph containing a given subset of nodes (terminals). In this paper we investigate applications of the linear matroid parity algorithm to the Steiner tree problem for two classes of graphs: where the terminals form a vertex cover and where terminals form a dominating set. As all these problems are MAX-SNP-hard, the issue is what approximation can be obtained in polynomial time. The previously best approximation ratio for the first class of graphs (also known as unweighted quasi-bipartite graphs) is ≈ 1.217 (Gröpl et al. [4]) is reduced in this paper to 8/7–1/160≈ 1.137. For the case of graphs where terminals form a dominating set, an approximation ratio of 4/3 is achieved.
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© 2006 Springer-Verlag Berlin Heidelberg
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Berman, P., Fürer, M., Zelikovsky, A. (2006). Applications of the Linear Matroid Parity Algorithm to Approximating Steiner Trees. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds) Computer Science – Theory and Applications. CSR 2006. Lecture Notes in Computer Science, vol 3967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753728_10
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DOI: https://doi.org/10.1007/11753728_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34166-6
Online ISBN: 978-3-540-34168-0
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