Chordal coloring algorithm.

Project.toml

@@ -12,13 +12,16 @@ 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]
 ADTypes = "1.2.1"
+CliqueTrees = "0.5.2"
 Colors = "0.12.11, 0.13"
 DataStructures = "0.18"
 DocStringExtensions = "0.8,0.9"

ext/SparseMatrixColoringsCliqueTreesExt.jl

@@ -0,0 +1,36 @@
+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(bg, 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

@@ -57,6 +57,7 @@ include("show_colors.jl")
 
 export NaturalOrder, RandomOrder, LargestFirst
 export DynamicDegreeBasedOrder, SmallestLast, IncidenceDegree, DynamicLargestFirst
+export PerfectEliminationOrder
 export ColoringProblem, GreedyColoringAlgorithm, AbstractColoringResult
 export ConstantColoringAlgorithm
 export coloring, fast_coloring

src/order.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

test/Project.toml

@@ -7,6 +7,7 @@ BlockArrays = "8e7c35d0-a365-5155-bbbb-fb81a777f24e"
 BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
 CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
 Chairmarks = "0ca39b1e-fe0b-4e98-acfc-b1656634c4de"
+CliqueTrees = "60701a23-6482-424a-84db-faee86b9b1f8"
 Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"

test/order.jl

@@ -1,3 +1,5 @@
+using CliqueTrees: CliqueTrees
+using BandedMatrices
 using LinearAlgebra
 using SparseArrays
 using SparseMatrixColorings
@@ -7,6 +9,7 @@ using SparseMatrixColorings:
     LargestFirst,
     NaturalOrder,
     RandomOrder,
+    PerfectEliminationOrder,
     degree_dist2,
     nb_vertices,
     valid_dynamic_order,
@@ -110,3 +113,18 @@ end;
         end
     end
 end;
+
+@testset "PerfectEliminationOrder" begin
+    problem1 = ColoringProblem(; structure=:symmetric, partition=:column)
+    problem2 = ColoringProblem(; structure=:nonsymmetric, partition=:column)
+    algorithm = GreedyColoringAlgorithm(
+        PerfectEliminationOrder(); decompression=:substitution
+    )
+
+    for (n, m) in ((800, 80), (400, 40), (200, 20), (100, 10))
+        perm = randperm(n)
+        matrix = permute!(sparse(Symmetric(brand(n, n, m, 0), :L)), perm, perm)
+        @test ncolors(coloring(matrix, problem1, algorithm)) == 1m + 1
+        @test ncolors(coloring(matrix, problem2, algorithm)) == 2m + 1
+    end
+end