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Speeding Up Dynamic Programming with Representative Sets

An Experimental Evaluation of Algorithms for Steiner Tree on Tree Decompositions

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Parameterized and Exact Computation (IPEC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8246))

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Abstract

Dynamic programming on tree decompositions is a frequently used approach to solve otherwise intractable problems on instances of small treewidth. In recent work by Bodlaender et al. [5], it was shown that for many connectivity problems, there exist algorithms that use time, linear in the number of vertices, and single exponential in the width of the tree decomposition that is used. The central idea is that it suffices to compute representative sets, and these can be computed efficiently with help of Gaussian elimination.

In this paper, we give an experimental evaluation of this technique for the Steiner Tree problem. A comparison of the classic dynamic programming algorithm and the improved dynamic programming algorithm that employs the table reduction shows that the new approach gives significant improvements on the running time of the algorithm and the size of the tables computed by the dynamic programming algorithm, and thus that the rank based approach from Bodlaender et al. [5] does not only give significant theoretical improvements but also is a viable approach in a practical setting, and showcases the potential of exploiting the idea of representative sets for speeding up dynamic programming algorithms.

The third author is supported by the NWO project ’Space and Time Efficient Structural Improvements of Dynamic Programming Algorithms’.

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Author information

Authors and Affiliations

  1. Utrecht University, The Netherlands

    Stefan Fafianie, Hans L. Bodlaender & Jesper Nederlof

Authors
  1. Stefan Fafianie
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  2. Hans L. Bodlaender
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  3. Jesper Nederlof
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Editor information

Editors and Affiliations

  1. Royal Holloway, University of London, Egham Hill, TW20 0EX, Egham, UK

    Gregory Gutin

  2. Institute of Information Systems, Vienna University of Technology, (184/3), Favoritenstraße 9-11, 1040, Vienna, Austria

    Stefan Szeider

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Fafianie, S., Bodlaender, H.L., Nederlof, J. (2013). Speeding Up Dynamic Programming with Representative Sets. In: Gutin, G., Szeider, S. (eds) Parameterized and Exact Computation. IPEC 2013. Lecture Notes in Computer Science, vol 8246. Springer, Cham. https://doi.org/10.1007/978-3-319-03898-8_27

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  • DOI: https://doi.org/10.1007/978-3-319-03898-8_27

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03897-1

  • Online ISBN: 978-3-319-03898-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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