Does this support data types other than graphs?

Yes, it supports any object in a C-set category, including hypergraphs, databases, simplicial complexes, and port graphs.

What is the benefit of the sheaf condition in this skill?

The sheaf condition ensures that local solutions found within individual decomposition bags can be correctly 'glued' together into a valid global solution.

How does this skill integrate with Julia?

It provides deep integration with the AlgebraicJulia ecosystem, specifically targeting StructuredDecompositions.jl, Catlab.jl, and SpecterACSet.jl.

What are structured decompositions used for?

They are used to solve computationally hard problems in linear time by breaking complex structures into tree-like arrangements of simpler parts, known as bags.

Structured Decomposition Engine

Name: Structured Decomposition Engine
Author: plurigrid

byplurigrid

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Ciencia de Datos y ML

Implements Fixed-Parameter Tractable (FPT) algorithms using sheaves on tree decompositions for compositional data structures.

The structured-decomp skill enables Claude to navigate and manipulate complex data structures like graphs, hypergraphs, and algebraic databases using category-theoretic principles. By leveraging Grothendieck topologies and the StructuredDecompositions.jl ecosystem, it allows for the implementation of compositional algorithms that solve decision problems in linear time for bounded-width inputs. It is ideal for developers and researchers working within AlgebraicJulia or categorical cybernetics who need to lift local solutions to global ones using bidirectional navigation and sheaf-theoretic gluing conditions.

Características Principales

01Automated lifting of decision problems to decomposition space using the 𝐃 functor

022 GitHub stars

03Support for FPT algorithms on graphs, hypergraphs, and metabolic networks

04Seamless integration with AlgebraicJulia, Catlab.jl, and ACSets

05S-expression serialization for decomposition inspection and round-tripping

06Bidirectional navigation of bags and adhesions via Specter-style paths

Casos de Uso

01Implementing categorical cybernetic systems using parameterized optics and sheaves

02Solving complex graph homomorphism or coloring problems on large datasets

03Decomposing metabolic networks for metabolic flux analysis (FBA)

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi structured-decomp

For use in Claude.ai and ChatGPT

Download Skill