Add ordering algorithm: PerfectEliminationOrder

Author: samuelsonric

Project.toml

@@ -5,17 +5,18 @@ version = "0.4.14"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
-CliqueTrees = "60701a23-6482-424a-84db-faee86b9b1f8"
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [weakdeps]
+CliqueTrees = "60701a23-6482-424a-84db-faee86b9b1f8"
 Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
 
 [extensions]
+SparseMatrixColoringsCliqueTreesExt = "CliqueTrees"
 SparseMatrixColoringsColorsExt = "Colors"
 
 [compat]

ext/SparseMatrixColoringsCliqueTreesExt.jl

@@ -0,0 +1,32 @@
+module SparseMatrixColoringsCliqueTreesExt
+
+using CliqueTrees: CliqueTrees
+using SparseArrays
+using SparseMatrixColorings: SparseMatrixColorings, AdjacencyGraph, BipartiteGraph, PerfectEliminationOrder, pattern
+
+function SparseMatrixColorings.vertices(g::AdjacencyGraph{T}, order::PerfectEliminationOrder) where T
+    S = pattern(g)
+
+    # construct matrix with sparsity pattern S
+    M = SparseMatrixCSC{Bool, T}(size(S)..., S.colptr, rowvals(S), ones(Bool, nnz(S)))
+
+    # can also use alg=CliqueTrees.LexBFS()
+    order, _ = CliqueTrees.permutation(M; alg=CliqueTrees.MCS())
+
+    return reverse!(order)
+end
+
+function SparseMatrixColorings.vertices(bg::BipartiteGraph{T}, ::Val{side}, order::PerfectEliminationOrder) where {T, side}
+    S = pattern(g, Val(side))
+
+    # construct matrix with sparsity pattern S
+    M = SparseMatrixCSC{Bool, T}(size(S)..., S.colptr, rowvals(S), ones(Bool, nnz(S)))
+
+    # can also use alg=CliqueTrees.LexBFS()
+    order, _ = CliqueTrees.permutation(M; alg=CliqueTrees.MCS())
+
+    return reverse!(order)
+
+end
+
+end # module

src/SparseMatrixColorings.jl

@@ -11,7 +11,6 @@ module SparseMatrixColorings
 
 using ADTypes: ADTypes
 using Base.Iterators: Iterators
-using CliqueTrees: CliqueTrees
 using DataStructures: DisjointSets, find_root!, root_union!, num_groups
 using DocStringExtensions: README, EXPORTS, SIGNATURES, TYPEDEF, TYPEDFIELDS
 using LinearAlgebra:
@@ -50,7 +49,6 @@ include("result.jl")
 include("matrices.jl")
 include("interface.jl")
 include("constant.jl")
-include("chordal.jl")
 include("adtypes.jl")
 include("decompression.jl")
 include("check.jl")
@@ -59,8 +57,9 @@ include("show_colors.jl")
 
 export NaturalOrder, RandomOrder, LargestFirst
 export DynamicDegreeBasedOrder, SmallestLast, IncidenceDegree, DynamicLargestFirst
+export PerfectEliminationOrder
 export ColoringProblem, GreedyColoringAlgorithm, AbstractColoringResult
-export ConstantColoringAlgorithm, ChordalColoringAlgorithm
+export ConstantColoringAlgorithm
 export coloring, fast_coloring
 export column_colors, row_colors, ncolors
 export column_groups, row_groups

src/chordal.jl

@@ -301,3 +301,17 @@ Instance of [`AbstractOrder`](@ref) which sorts vertices from lowest to highest
 - [`DynamicDegreeBasedOrder`](@ref)
 """
 const DynamicLargestFirst = DynamicDegreeBasedOrder{:forward,:low2high}
+
+"""
+    PerfectEliminationOrder
+
+Instance of [`AbstractOrder`](@ref) which sorts the vertices of a chordal graph in a perfect elimination order.
+
+!!! danger
+    This order is implemented as a package extension and requires loading CliqueTrees.jl.
+
+# References
+
+- [Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs](https://epubs.siam.org/doi/10.1137/0213035), Tarjan and Yannakakis (1984)
+"""
+struct PerfectEliminationOrder <: AbstractOrder end