# Practical Access to Dynamic Programming on Tree Decompositions

arXiv: https://arxiv.org/abs/1806.10176 · HTML: https://mlsanity.com/paper/1806.10176/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2018.

## Built on by (most cited first, 5 of 5)

- [Treewidth-aware Reductions of Normal ASP to SAT -- Is Normal ASP Harder than SAT after All?](https://mlsanity.com/paper/2210.03553/) (2022)
- [Advanced Tools and Methods for Treewidth-Based Problem Solving -- Extended Abstract](https://mlsanity.com/paper/2208.11340/) (2022)
- [Solving Projected Model Counting by Utilizing Treewidth and its Limits](https://mlsanity.com/paper/2305.19212/) (2023)
- [From Width-Based Model Checking to Width-Based Automated Theorem Proving](https://mlsanity.com/paper/2205.10995/) (2022)
- [Exact Algorithms for Multiagent Path Finding with Communication Constraints on Tree-Like Structures](https://mlsanity.com/paper/2412.08556/) (2024)

## Abstract (arXiv)

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.