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samuelsonricgdalle
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Chordal coloring algorithm (#202)
* Add chordal coloring. * fix bug * Add ordering algorithm: `PerfectEliminationOrder` * Add tests for ordering algorithm `PerfectEliminationOrder`. * Respond to PR comments. * Add `PerfectEliminationOrder` to api. * Update src/order.jl * Update src/order.jl * Update src/order.jl * Fix docstring * Bump version * Make elimination algorithm parametric * Only substitution --------- Co-authored-by: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
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‎Project.toml‎

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name = "SparseMatrixColorings"
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uuid = "0a514795-09f3-496d-8182-132a7b665d35"
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authors = ["Guillaume Dalle", "Alexis Montoison"]
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version = "0.4.14"
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version = "0.4.15"
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[deps]
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ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
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SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
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[weakdeps]
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CliqueTrees = "60701a23-6482-424a-84db-faee86b9b1f8"
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Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
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[extensions]
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SparseMatrixColoringsCliqueTreesExt = "CliqueTrees"
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SparseMatrixColoringsColorsExt = "Colors"
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[compat]
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ADTypes = "1.2.1"
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CliqueTrees = "0.5.2"
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Colors = "0.12.11, 0.13"
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DataStructures = "0.18"
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DocStringExtensions = "0.8,0.9"

‎docs/Project.toml‎

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Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0"
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SparseMatrixColorings = "0a514795-09f3-496d-8182-132a7b665d35"
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StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
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[sources]
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SparseMatrixColorings = {path=".."}

‎docs/src/api.md‎

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IncidenceDegree
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DynamicLargestFirst
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DynamicDegreeBasedOrder
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PerfectEliminationOrder
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```

‎ext/SparseMatrixColoringsCliqueTreesExt.jl‎

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module SparseMatrixColoringsCliqueTreesExt
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import CliqueTrees: permutation, EliminationAlgorithm, MCS
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import SparseArrays: SparseMatrixCSC, rowvals, nnz
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import SparseMatrixColorings:
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AdjacencyGraph, BipartiteGraph, PerfectEliminationOrder, pattern, vertices
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PerfectEliminationOrder() = PerfectEliminationOrder(MCS())
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function vertices(g::AdjacencyGraph{T}, order::PerfectEliminationOrder) where {T}
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S = pattern(g)
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# construct matrix with sparsity pattern S
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M = SparseMatrixCSC{Bool,T}(size(S)..., S.colptr, rowvals(S), ones(Bool, nnz(S)))
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# construct a perfect elimination order
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# self-loops are ignored
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order, _ = permutation(M; alg=order.elimination_algorithm)
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return reverse!(order)
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end
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end # module

‎src/SparseMatrixColorings.jl‎

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export NaturalOrder, RandomOrder, LargestFirst
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export DynamicDegreeBasedOrder, SmallestLast, IncidenceDegree, DynamicLargestFirst
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export PerfectEliminationOrder
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export ColoringProblem, GreedyColoringAlgorithm, AbstractColoringResult
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export ConstantColoringAlgorithm
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export coloring, fast_coloring

‎src/order.jl‎

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- [`IncidenceDegree`](@ref) (experimental)
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- [`SmallestLast`](@ref) (experimental)
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- [`DynamicLargestFirst`](@ref) (experimental)
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- [`PerfectEliminationOrder`](@ref)
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"""
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abstract type AbstractOrder end
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- [`DynamicDegreeBasedOrder`](@ref)
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"""
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const DynamicLargestFirst = DynamicDegreeBasedOrder{:forward,:low2high}
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"""
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PerfectEliminationOrder(elimination_algorithm=CliqueTrees.MCS())
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Instance of [`AbstractOrder`](@ref) which computes a perfect elimination ordering when the underlying graph is [chordal](https://en.wikipedia.org/wiki/Chordal_graph). For non-chordal graphs, it computes a suboptimal ordering.
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The `elimination_algorithm` must be an instance of `CliqueTrees.EliminationAlgorithm`.
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!!! warning
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This order can only be applied for symmetric or bidirectional coloring problems. Furthermore, its theoretical guarantees only hold for decompression by substitution.
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!!! danger
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This order is implemented as a package extension and requires loading [CliqueTrees.jl](https://github.com/AlgebraicJulia/CliqueTrees.jl).
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# References
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- [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)
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"""
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struct PerfectEliminationOrder{E} <: AbstractOrder
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elimination_algorithm::E
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end

‎test/Project.toml‎

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

‎test/order.jl‎

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using CliqueTrees: CliqueTrees
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using BandedMatrices
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using LinearAlgebra
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using SparseArrays
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using SparseMatrixColorings
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LargestFirst,
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NaturalOrder,
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RandomOrder,
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PerfectEliminationOrder,
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degree_dist2,
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nb_vertices,
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valid_dynamic_order,
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end
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end
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end;
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@testset "PerfectEliminationOrder" begin
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problem = ColoringProblem(; structure=:symmetric, partition=:column)
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substitution_algo = GreedyColoringAlgorithm(
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PerfectEliminationOrder(); decompression=:substitution
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)
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# band graphs
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for (n, m) in ((800, 80), (400, 40), (200, 20), (100, 10))
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perm = randperm(rng, n)
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matrix = permute!(sparse(Symmetric(brand(n, n, m, 0), :L)), perm, perm)
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π = vertices(AdjacencyGraph(matrix), PerfectEliminationOrder())
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@test isperm(π)
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@test ncolors(coloring(matrix, problem, substitution_algo)) == m + 1
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end
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# random graphs
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for (n, p) in Iterators.product(20:20:100, 0.0:0.1:0.2)
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matrix = sparse(Symmetric(sprand(rng, Bool, n, n, p)))
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π = vertices(AdjacencyGraph(matrix), PerfectEliminationOrder())
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@test isperm(π)
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end
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end

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