Add chordal coloring.

Author: samuelsonric

Project.toml

@@ -5,6 +5,7 @@ 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"
@@ -19,6 +20,7 @@ SparseMatrixColoringsColorsExt = "Colors"
 
 [compat]
 ADTypes = "1.2.1"
+CliqueTrees = "0.5.2"
 Colors = "0.12.11, 0.13"
 DataStructures = "0.18"
 DocStringExtensions = "0.8,0.9"

src/SparseMatrixColorings.jl

@@ -11,6 +11,7 @@ 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:
@@ -49,6 +50,7 @@ include("result.jl")
 include("matrices.jl")
 include("interface.jl")
 include("constant.jl")
+include("chordal.jl")
 include("adtypes.jl")
 include("decompression.jl")
 include("check.jl")
@@ -58,7 +60,7 @@ include("show_colors.jl")
 export NaturalOrder, RandomOrder, LargestFirst
 export DynamicDegreeBasedOrder, SmallestLast, IncidenceDegree, DynamicLargestFirst
 export ColoringProblem, GreedyColoringAlgorithm, AbstractColoringResult
-export ConstantColoringAlgorithm
+export ConstantColoringAlgorithm, ChordalColoringAlgorithm
 export coloring, fast_coloring
 export column_colors, row_colors, ncolors
 export column_groups, row_groups

src/chordal.jl

@@ -0,0 +1,29 @@
+struct ChordalColoringAlgorithm <: ADTypes.AbstractColoringAlgorithm end
+
+struct ChordalColoringResult{M <: AbstractMatrix, V} <: AbstractColoringResult{:symmetric, :column, :direct}
+    A::M
+    color::Vector{Int}
+    group::V
+end
+
+function coloring(
+    A::AbstractMatrix,
+    ::ColoringProblem{:symmetric,:column},
+    algo::ChordalColoringAlgorithm,
+)
+    # compute an elimination ordering using
+    # the maximum cardinality search algorithm
+    perm, invp = CliqueTrees.permutation(A; alg=CliqueTrees.MCS())
+    
+    # if the ordering is not perfect, then the graph is not chordal
+    if !CliqueTrees.isperfect(A, perm, invp)
+        error("Matrix does not have a chordal sparsity pattern.")
+    end
+
+    # if the graph is chordal, then find a minimal vertex coloring
+    color = CliqueTrees.color(A, invp).colors
+
+    # compute groups and return result
+    group = group_by_color(color)
+    return ChordalColoringResult(A, color, group)
+end