We introduce structured decompositions: category-theoretic generalizations of many combinatorial invariants -- including tree-width, layered tree-width, co-tree-width 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 algorithmically useful structural compositionality. As an application of our theory we prove an algorithmic meta theorem for the Sub_P-composition problem which, when instantiated in the category of graphs, yields compositional algorithms for NP-hard problems such as: Maximum Bipartite Subgraph, Maximum Planar Subgraph and Longest Path.

翻译：我们引入了结构分解法:对许多组合式结构变异物(包括树枝、分层树枝、共同树枝和图形分解宽度)进行分类理论集,这在图形理论和参数化复杂度的结构和算法组成性研究中发挥了中心作用。结构分解法使我们能够将组合变异物归纳到新的环境(例如对类固醇的分解)中,在这种环境中,它们描述了逻辑学上有用的结构组成性。作为我们理论的应用,我们证明了子-P组化问题的算法元理论。 当在图形类别中即刻出现时,可产生NP-硬性问题(例如:最大双部分分计、最大平面分算法和最长路径)的合成算法。