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Algorithms for computing or approximating optimal decompositions fordecompositional parameters such as treewidth or clique-width have so fartraditionally been tailored to specific width parameters. Moreover, formim-width, no efficient algorithms for computing good decompositions wereknown, even under highly restrictive parameterizations. In this work weidentify F-branchwidth as a class of generic decompositional parameters thatcan capture mim-width, treewidth, clique-width as well as other measures. Weshow that while there is an infinite number of F-branchwidth parameters, only ahandful of these are asymptotically distinct. We then develop fixed-parameterand kernelization algorithms (under several structural parameterizations) thatcan compute every possible F-branchwidth, providing a unifying framework thatcan efficiently obtain near-optimal tree-decompositions, k-expressions, as wellas optimal mim-width decompositions.

A Unifying Framework for Characterizing and Computing Width Measures