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Embedding Complexity and Discrete Optimization II: A Dynamical Programming Approach to the Steiner-Tree Problem
D. Cieslik1, A. Dress2, K.T. Huber3, and V. Moulton4
1Institute of Mathematics and Computer Science, University of Greifswald, 17487 Greifswald Germany
cieslik@mail.uni-greifswald.de
2FSPM-Strukturbildungsprozesse, University of Bielefeld, 33501 Bielefeld, Germany
dress@mathematik.uni-bielefeld.de
3Department of Biometry and Informatics, Swedish University of Agricultural Sciences, 75007 Uppsala, Sweden
katharina.huber@bi.slu.se
4Linnaeus Center for Bioinformatics, Uppsala University, BMC, Box 598, 75124 Uppsala Sweden
vincent.moulton@lcb.uu.se
Annals of Combinatorics 6 (3) p.275-283 September, 2002
AMS Subject Classification: 90C39, 05C05, 68W99
Abstract:
In this note, we continue our work devoted to investigating the concept of embedding complexity (cf. Cieslik et al. [3]) and present a new Divide and Conquer algorithm for solving the Steiner-tree problem for graphs that relies on dynamic-programming schemes. In this way, we show how the rather general conceptual framework developed in our previous paper can be used even in rather awkward situations and that, more specifically, it allows us to design a treewidth-based algorithm for finding Steiner trees in a (weighted or unweighted) graph that is linear with respect to the number of the graph's vertices, yet (as we cannot avoid paying the ``standard fine'' set on using treewidth-based algorithms) highly exponential with respect to the graph's treewidth.
Keywords: Optimization, discrete optimization, Divide and Conquer, dynamic programming, dynamic-programming schemes, computational complexity, algorithmic complexity, structural complexity, embedding complexity, treewidth, Steiner's problem, Steiner minimal trees, SMT

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