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Practical Access to Dynamic Programming on Tree Decompositions

Authors Max Bannach , Sebastian Berndt



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LIPIcs.ESA.2018.6.pdf
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Author Details

Max Bannach
  • Institute for Theoretical Computer Science, Universität zu Lübeck, Lübeck, Germany
Sebastian Berndt
  • Department of Computer Science, Kiel University, Kiel, Germany

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Max Bannach and Sebastian Berndt. Practical Access to Dynamic Programming on Tree Decompositions. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 6:1-6:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ESA.2018.6

Abstract

Parameterized complexity theory has lead to a wide range of algorithmic breakthroughs within the last decades, but the practicability of these methods for real-world problems is still not well understood. We investigate the practicability of one of the fundamental approaches of this field: dynamic programming on tree decompositions. Indisputably, this is a key technique in parameterized algorithms and modern algorithm design. Despite the enormous impact of this approach in theory, it still has very little influence on practical implementations. The reasons for this phenomenon are manifold. One of them is the simple fact that such an implementation requires a long chain of non-trivial tasks (as computing the decomposition, preparing it,...). We provide an easy way to implement such dynamic programs that only requires the definition of the update rules. With this interface, dynamic programs for various problems, such as 3-coloring, can be implemented easily in about 100 lines of structured Java code. The theoretical foundation of the success of dynamic programming on tree decompositions is well understood due to Courcelle's celebrated theorem, which states that every MSO-definable problem can be efficiently solved if a tree decomposition of small width is given. We seek to provide practical access to this theorem as well, by presenting a lightweight model-checker for a small fragment of MSO. This fragment is powerful enough to describe many natural problems, and our model-checker turns out to be very competitive against similar state-of-the-art tools.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • fixed-parameter tractability
  • treewidth
  • model-checking

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References

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