# Structured Decompositions: Structural and Algorithmic Compositionality

@article{Bumpus2022StructuredDS, title={Structured Decompositions: Structural and Algorithmic Compositionality}, author={Benjamin Merlin Bumpus and Zoltan A. Kocsis and Jade Edenstar Master}, journal={ArXiv}, year={2022}, volume={abs/2207.06091} }

We introduce structured decompositions: category-theoretic generalizations of many combinatorial invariants – including tree-width, layered tree-width, co-treewidth and graph decomposition width – which have played a central role in the study of structural and algorithmic compositionality in both graph theory and parameterized complexity. Structured decompositions allow us to generalize combinatorial invariants to new settings (for example decompositions of matroids) in which they describe…

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