2000 character limit reached
Structured Decompositions: Structural and Algorithmic Compositionality (2207.06091v7)
Published 13 Jul 2022 in math.CT, cs.DS, and math.CO
Abstract: 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.
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.