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Open AccessArticle

Practical Access to Dynamic Programming on Tree Decompositions

1
Institute for Theoretical Computer Science, Universität zu Lübeck, 23562 Lübeck, Germany
2
Department of Computer Science, Kiel University, 24103 Kiel, Germany
*
Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in ESA 2018.
Algorithms 2019, 12(8), 172; https://doi.org/10.3390/a12080172
Received: 18 July 2019 / Revised: 5 August 2019 / Accepted: 13 August 2019 / Published: 16 August 2019
(This article belongs to the Special Issue New Frontiers in Parameterized Complexity and Algorithms)
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Abstract

Parameterized complexity theory has led to a wide range of algorithmic breakthroughs within the last few 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 1 (that is, we do not consider “edge-set-based” problems). 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. View Full-Text
Keywords: fixed-parameter tractability; treewidth; model checking fixed-parameter tractability; treewidth; model checking
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Bannach, M.; Berndt, S. Practical Access to Dynamic Programming on Tree Decompositions. Algorithms 2019, 12, 172.

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