Structured Decompositions: Structural and Algorithmic Compositionality
Category Theory
2025-05-21 v7 Data Structures and Algorithms
Combinatorics
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.
Cite
@article{arxiv.2207.06091,
title = {Structured Decompositions: Structural and Algorithmic Compositionality},
author = {Benjamin Merlin Bumpus and Zoltan A. Kocsis and Jade Edenstar Master and Emilio Minichiello},
journal= {arXiv preprint arXiv:2207.06091},
year = {2025}
}
Comments
This version is a major rewrite. 35 pages and an appendix. Comments and suggestions welcome!