Speeding up the Dreyfus–Wagner algorithm for minimum Steiner trees

Bernhard Fuchs (), Walter Kern () and Xinhui Wang ()

Mathematical Methods of Operations Research, 2007, vol. 66, issue 1, 117-125

Abstract: The Dreyfus–Wagner algorithm is a well-known dynamic programming method for computing minimum Steiner trees in general weighted graphs in time O * (3 k ), where k is the number of terminal nodes to be connected. We improve its running time to O * (2.684 k ) by showing that the optimum Steiner tree T can be partitioned into T = T 1 ∪ T 2 ∪ T 3 in a certain way such that each T i is a minimum Steiner tree in a suitable contracted graph G i with less than $${\frac{k}{2}}$$ terminals. In the rectilinear case, there exists a variant of the dynamic programming method that runs in O * (2.386 k ). In this case, our splitting technique yields an improvement to O * (2.335 k ). Copyright Springer-Verlag 2007

Keywords: Steiner tree; Exact algorithm; Dynamic programming (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s00186-007-0146-0

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