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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データサイエンスとML

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

概要

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.

主な機能

Automated lifting of decision problems to decomposition space using the 𝐃 functor
2 GitHub stars
Support for FPT algorithms on graphs, hypergraphs, and metabolic networks
Seamless integration with AlgebraicJulia, Catlab.jl, and ACSets
S-expression serialization for decomposition inspection and round-tripping
Bidirectional navigation of bags and adhesions via Specter-style paths

ユースケース

Implementing categorical cybernetic systems using parameterized optics and sheaves
Solving complex graph homomorphism or coloring problems on large datasets
Decomposing metabolic networks for metabolic flux analysis (FBA)

概要

主な機能

Automated lifting of decision problems to decomposition space using the 𝐃 functor
2 GitHub stars
Support for FPT algorithms on graphs, hypergraphs, and metabolic networks
Seamless integration with AlgebraicJulia, Catlab.jl, and ACSets
S-expression serialization for decomposition inspection and round-tripping
Bidirectional navigation of bags and adhesions via Specter-style paths

ユースケース

Implementing categorical cybernetic systems using parameterized optics and sheaves
Solving complex graph homomorphism or coloring problems on large datasets
Decomposing metabolic networks for metabolic flux analysis (FBA)