Elsevier

Journal of Discrete Algorithms

Volume 16, October 2012, Pages 67-78
Journal of Discrete Algorithms

Improved Steiner tree algorithms for bounded treewidth

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Abstract

We propose a new algorithm that solves the Steiner tree problem on graphs with vertex set V to optimality in O(Btw+22tw|V|) time, where tw is the graphʼs treewidth and the Bell number Bk is the number of partitions of a k-element set. This is a linear-time algorithm for graphs with fixed treewidth and a polynomial algorithm for twO(log|V|/loglog|V|).

While being faster than the previously known algorithms, the coloring scheme used in our algorithm can be extended to give new, improved algorithms for the prize-collecting Steiner tree as well as the k-cardinality tree problems with similar runtime bounds.

Keywords

(Prize-collecting) Steiner tree
k-Cardinality tree
Bounded treewidth
Fixed parameter tractable
Exact algorithm

Cited by (0)

A preliminary version of this article appeared at IWOCA 2011, LNCS, vol. 7056, Springer, 2011, pp. 374–386.

1

Funded via a juniorprofessorship by the Carl-Zeiss-Foundation.