Lift graph decision problems into decomposition spaces using StrDecomp.
npx skills add https://github.com/plurigrid/asi --skill structured-decomp
Please help me install this Agent Skill. Skill: structured-decomp Source: https://github.com/plurigrid/asi/tree/main/skills/structured-decomp Command: npx skills add https://github.com/plurigrid/asi --skill structured-decomp
Uses tree decompositions and sheaf-theoretic ideas to enable efficient, structured decompositions for algorithmic problems.
Load a graph, create a decomposition, and inspect bags and adhesions.
High-intent search queries and answers about installing and using this skill.
Tree decomposition lifts graph problems into a structured space where algorithms run in FPT time O(f(width) * n), governed by adhesion width. StrDecomp enables this by accepting a graph, a functor representing your problem, and a decomposition strategy, then producing solutions through bags and adhesions.
FPT algorithms solve NP-hard graph problems like colorings and decision problems on graphs with bounded treewidth or adhesion. Tree decomposition expresses these as functors, making them tractable on narrow graphs where width-dependent runtime dominates.
Bags partition graph vertices, adhesions are their intersections across bags, and spans connect them bidirectionally. StrDecomp provides navigation through these structures so you inspect decomposition geometry and apply functors locally at each bag.
Yes, decompositions integrate with lispsyntax-acset to serialize bags, adhesions, and spans for inspection and round-tripping, enabling reproducible analysis and debugging of decomposition structure.
StrDecomp accepts a graph input along with a StrDecomp instance, a problem functor, and a target decomposition strategy like CoDecomposition. The framework then decomposes and solves the problem in FPT time.
Use sheaf-theoretic decomposition for problems on graphs with bounded width where FPT runtime O(f(width) * n) is faster than polynomial approaches. It scales on narrow graphs and supports problems expressible as functors over decompositions.
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