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Structured Decompositions: Structural and Algorithmic Compositionality
Benjamin Merlin Bumpus, Zoltan A. Kocsis, Jade Edenstar Master, Emilio Minichiello
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We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number, hypergraph treewidth and H-treewidth), geometric group theory (specifically Bass-Serre theory), and dynamical systems (e.g. hybrid dynamical systems). We define width functors, which provide a compositional way to analyze and relate different structural complexity measures, and establish a general duality between decompositions and completions of objects.
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