[blegat]

Reuse the existing CSC write logic for one-edge trees, whose value can be read directly from the compressed matrix without substitution. Move that logic into a helper shared by the one-edge case and the general substitution path.

Small recovery benchmark for 250 dense 20×20 blocks, run with SMC before and after this change:

using BenchmarkTools, LinearAlgebra, SparseArrays, Statistics
import SparseMatrixColorings as SMC

A = kron(spdiagm(0 => ones(250)), sparse(ones(20, 20)))
result = SMC.coloring(
    SMC.SparsityPatternCSC(A),
    SMC.ColoringProblem(; structure=:symmetric),
    SMC.GreedyColoringAlgorithm(; decompression=:substitution),
)
B = Matrix(SMC.compress(A, result))
L = tril(A)
values, colptr = similar(nonzeros(L)), L.colptr
trial = @benchmark SMC.decompress_csc!($values, $colptr, $B, $result, :L) evals=1
@assert values ≈ nonzeros(L)
display(median(trial))

Measured medians for the same block pattern (5,000 variables); full Hessian evaluation was benchmarked separately through MOI:

Implementation	Recovery only	Full Hessian
Legacy MOI	98.98 μs	521.63 μs
SMC before	252.67 μs	662.93 μs
SMC after	143.89 μs	527.16 μs

On Julia 1.13.1 with Intel i7-12700K.

[codecov]

Codecov Report

❌ Patch coverage is 1.81818% with 108 lines in your changes missing coverage. Please review.
✅ Project coverage is 43.40%. Comparing base (7d894ca) to head (9bb0e21).

Files with missing lines	Patch %	Lines
src/decompression.jl	0.00%	108 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #354      +/-   ##
==========================================
- Coverage   46.91%   43.40%   -3.51%     
==========================================
  Files          20       20              
  Lines        2498     2534      +36     
==========================================
- Hits         1172     1100      -72     
- Misses       1326     1434     +108     

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[amontoison]

@blegat Can you do the same modification for the acyclic bicoloring?
The title of the PR is also wrong now.

[amontoison]

@blegat You also forgot to update the method decompress!(A::AbstractMatrix, B, ::TreeSetColoringResult, uplo). I can merge the PR after that.

[amontoison]

@blegat
We have a typo in the docstring of is_star (src/coloring.jl, struct TreeSet): "three" should be "tree".

"For a tree index `1 <= k <= nt`, `is_star[k]` indicates whether the `k`th tree is a star."

I also want to fix a comment in the TreeSet constructor (src/coloring.jl, where first_vertex and last_vertex are computed).
This one predates the PR, but while we are here: "so we add to add an offset" is a typo, and the comment doesn't say why the offset is needed.
I suggest:

# Note: tree_edge_indices contains the positions of the first and last edges.
# Each tree has one more vertex than edges, so the k-1 previous trees shift
# the vertex positions by k-1 with respect to the edge positions.