From 40a4ffe4c3e70ae78b1b1339c110f44d3928d72b Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Wed, 25 Sep 2024 17:16:08 +0000 Subject: [PATCH] build based on 2086dbe --- dev/.documenter-siteinfo.json | 2 +- dev/api/index.html | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 2345653..9e3dc41 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-25T17:16:00","documenter_version":"1.7.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-25T17:16:05","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/dev/api/index.html b/dev/api/index.html index 2a5b881..3391b5d 100644 --- a/dev/api/index.html +++ b/dev/api/index.html @@ -1,2 +1,2 @@ -Library Reference · StructuredDecompositions.jl
GitHub

Library Reference

StructuredDecompositions.Decompositions.StrDecomp — Method

One can construct a structured decomposition by simply providing the graph representing the shape of the decompostion and the relevant diagram. This constructor will default to setting the Decompsotion Type to Decomposition (i.e. we default to viewing C-valued structured decompositions as diagrams into Span C)

source
StructuredDecompositions.Decompositions.𝐃 — Function

The construction of categories of structured decompostions is functorial; it consists of a functor 𝐃: Cat{pullback} → Cat taking any category C with pullbacks to the category 𝐃C of C-values structured decompositions. The functoriality of this construction allows us to lift any functor F : C → E to a functor 𝐃f : 𝐃 C → 𝐃 E which maps C-valued structured decompositions to E-valued structured decompositions. When we think of the functor F as a computational problem (taking inputs in C to solution spaces in E), then 𝐃f should be thought of as lifting the global comuputation of F to local computation on the constituent parts of C-valued decompositions. In particular, given a structured decomposition d: FG → C and a sheaf F: C → FinSet^{op} w.r.t to the decompositon topology, we can make a structured decomposition valued in FinSet^{op} by lifting the sheaf to a functor 𝐃f: 𝐃C → 𝐃(S^{op}) between categories of structured decompositions.

source
StructuredDecompositions.DecidingSheaves.adhesion_filter — Method

Filtering algorithm. Note: we are assuming that we only know how to work with FinSet(Int) !

INPUT: a Finset^{op}-valued structured decomposition d : FG → Span Finset^{op} (which is expected to be in co-decomposition form; i.e. as a diagram d : FG → Cospan Finset ) and an indexed span ( (ℓ, r), ( d(ℓ), d(r) ) ) in d (i.e a pair consisting of span (ℓ, r) in ∫G and its image under d)

OUTPUT: a structured decomposition obtained by replacing the span de in d by the span obtained by projecting the pullback of de (i.e. taking images)

source
StructuredDecompositions.DecidingSheaves.decide_sheaf_tree_shape — Function

Solve the decision problem encoded by a sheaf. The algorithm is as follows: compute on each bag (optionally, if the decomposition of the solution space is already known, then it can be passed as an argument), compute composites on edges, project back down to bags answer (providing a witness) "no" if there is an empty bag; "yes" otherwise.

source
+Library Reference · StructuredDecompositions.jl
GitHub

Library Reference

StructuredDecompositions.Decompositions.StrDecomp — Method

One can construct a structured decomposition by simply providing the graph representing the shape of the decompostion and the relevant diagram. This constructor will default to setting the Decompsotion Type to Decomposition (i.e. we default to viewing C-valued structured decompositions as diagrams into Span C)

source
StructuredDecompositions.Decompositions.𝐃 — Function

The construction of categories of structured decompostions is functorial; it consists of a functor 𝐃: Cat{pullback} → Cat taking any category C with pullbacks to the category 𝐃C of C-values structured decompositions. The functoriality of this construction allows us to lift any functor F : C → E to a functor 𝐃f : 𝐃 C → 𝐃 E which maps C-valued structured decompositions to E-valued structured decompositions. When we think of the functor F as a computational problem (taking inputs in C to solution spaces in E), then 𝐃f should be thought of as lifting the global comuputation of F to local computation on the constituent parts of C-valued decompositions. In particular, given a structured decomposition d: FG → C and a sheaf F: C → FinSet^{op} w.r.t to the decompositon topology, we can make a structured decomposition valued in FinSet^{op} by lifting the sheaf to a functor 𝐃f: 𝐃C → 𝐃(S^{op}) between categories of structured decompositions.

source
StructuredDecompositions.DecidingSheaves.adhesion_filter — Method

Filtering algorithm. Note: we are assuming that we only know how to work with FinSet(Int) !

INPUT: a Finset^{op}-valued structured decomposition d : FG → Span Finset^{op} (which is expected to be in co-decomposition form; i.e. as a diagram d : FG → Cospan Finset ) and an indexed span ( (ℓ, r), ( d(ℓ), d(r) ) ) in d (i.e a pair consisting of span (ℓ, r) in ∫G and its image under d)

OUTPUT: a structured decomposition obtained by replacing the span de in d by the span obtained by projecting the pullback of de (i.e. taking images)

source
StructuredDecompositions.DecidingSheaves.decide_sheaf_tree_shape — Function

Solve the decision problem encoded by a sheaf. The algorithm is as follows: compute on each bag (optionally, if the decomposition of the solution space is already known, then it can be passed as an argument), compute composites on edges, project back down to bags answer (providing a witness) "no" if there is an empty bag; "yes" otherwise.

source