JunctionTrees and NestedUWDs

Project.toml

@@ -1,15 +1,22 @@
 name = "StructuredDecompositions"
 uuid = "ba32925c-6e4c-4640-bed9-b00febeea19a"
 authors = ["benjaminmerlinbumpus <[email protected]>"]
-version = "0.1.0"
+version = "0.2.0"
 
 [deps]
+AMD = "14f7f29c-3bd6-536c-9a0b-7339e30b5a3e"
+AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
 Catlab = "134e5e36-593f-5add-ad60-77f754baafbe"
+CuthillMcKee = "17f17636-5e38-52e3-a803-7ae3aaaf3da9"
+DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MLStyle = "d8e11817-5142-5d16-987a-aa16d5891078"
+Metis = "2679e427-3c69-5b7f-982b-ece356f1e94b"
 PartialFunctions = "570af359-4316-4cb7-8c74-252c00c2016b"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [compat]
-Catlab = "^0.14"
-MLStyle = "^0.4"
-PartialFunctions = "^1.1"
-julia = "^1.7"
+Catlab = "0.16"
+MLStyle = "0.4"
+PartialFunctions = "1.1"
+julia = "1.7"

src/Decompositions.jl

@@ -139,8 +139,8 @@ adhesionSpans(d)      = adhesionSpans(d, false)
 
 function elements_graph(el::Elements)
   F = FinFunctor(Dict(:V => :El, :E => :Arr), Dict(:src => :src, :tgt => :tgt), SchGraph, SchElements)
-  ΔF = DeltaMigration(F, Elements{Symbol}, Graph)
-  return ΔF(el)
+  ΔF = DeltaMigration(F)
+  return migrate(Graph, el, ΔF)
 end
 
 """Syntactic sugar for costrucitng the category of elements of a graph. 
@@ -152,8 +152,8 @@ function ∫(G::Elements)             FinCat(elements_graph(G)) end
 #reverse direction of the edges
 function op_graph(g::Graph)::Graph
   F = FinFunctor(Dict(:V => :V, :E => :E), Dict(:src => :tgt, :tgt => :src), SchGraph, SchGraph)
-  ΔF = DeltaMigration(F, Graph, Graph)
-  return ΔF(g)
+  ΔF = DeltaMigration(F)
+  return migrate(Graph, g, ΔF)
 end
 
 """

src/StructuredDecompositions.jl

@@ -4,6 +4,8 @@ module StructuredDecompositions
 include("Decompositions.jl")
 include("FunctorUtils.jl")
 include("DecidingSheaves.jl")
+include("junction_trees/JunctionTrees.jl")
+include("nested_uwds/NestedUWDs.jl")
 
 
 end 

src/junction_trees/JunctionTrees.jl

@@ -0,0 +1,83 @@
+module JunctionTrees
+
+
+import AMD
+import CuthillMcKee
+import Metis
+
+using AbstractTrees
+using Catlab.BasicGraphs
+using DataStructures
+using SparseArrays
+
+# Elimination Algorithms
+export EliminationAlgorithm, AMDJL_AMD, CuthillMcKeeJL_RCM, MetisJL_ND, MCS
+
+# Supernodes
+export Supernode, Node, MaximalSupernode, FundamentalSupernode
+
+# Orders
+export Order
+
+# Elimination Trees
+export EliminationTree
+export getwidth, getsupernode, getsubtree, getlevel
+
+# Junction Trees
+export JunctionTree
+export getseperator, getresidual
+
+
+# Add an element x to a sorted set v.
+# Returns true if x ∉ v.
+# Returns false if x ∈ v.
+function insertsorted!(v::Vector, x::Integer)
+    i = searchsortedfirst(v, x)
+
+    if i > length(v) || v[i] != x
+        insert!(v, i, x)
+        true
+    else
+        false
+    end
+end
+
+
+# Delete an element x from a sorted set v.
+# Returns true if x ∈ v.
+# Returns false if x ∉ v.
+function deletesorted!(v::Vector, x::Integer)
+    i = searchsortedfirst(v, x)
+
+    if i <= length(v) && v[i] == x
+        deleteat!(v, i)
+        true
+    else
+        false
+    end
+end
+
+
+# Delete the elements xs from a sorted set v.
+# Returns true if xs and v intersect.
+# Returns false if xs and v are disjoint.
+function deletesorted!(v::Vector, xs::AbstractVector)
+    isintersecting = true
+
+    for x in xs
+        isintersecting = deletesorted!(v, x) || isintersecting
+    end
+
+    isintersecting
+end
+
+
+include("elimination_algorithms.jl")
+include("supernodes.jl")
+include("orders.jl")
+include("trees.jl")
+include("elimination_trees.jl")
+include("junction_trees.jl")
+
+
+end

src/junction_trees/elimination_algorithms.jl

@@ -0,0 +1,45 @@
+"""
+    EliminationAlgorithm
+
+A graph elimination algorithm. The options are
+- [`CuthillMcKeeJL_RCM`](@ref)
+- [`AMDJL_AMD`](@ref)
+- [`MetisJL_ND`](@ref)
+- [`MCS`](@ref)
+"""
+abstract type EliminationAlgorithm end
+
+
+"""
+    CuthillMcKeeJL_RCM <: EliminationAlgorithm
+
+The reverse Cuthill-McKee algorithm. Uses CuthillMckee.jl.
+"""
+struct CuthillMcKeeJL_RCM <: EliminationAlgorithm end
+
+
+"""
+    AMDJL_AMD <: EliminationAlgorithm
+
+The approximate minimum degree algorithm. Uses AMD.jl.
+"""
+struct AMDJL_AMD <: EliminationAlgorithm end
+
+
+"""
+    MetisJL_ND <: EliminationAlgorithm
+
+The nested dissection heuristic. Uses Metis.jl.
+"""
+struct MetisJL_ND <: EliminationAlgorithm end
+
+
+"""
+    MCS <: EliminationAlgorithm
+
+The maximum cardinality search algorithm.
+"""
+struct MCS <: EliminationAlgorithm end
+
+
+const DEFAULT_ELIMINATION_ALGORITHM = AMDJL_AMD()