diff --git a/Project.toml b/Project.toml
index 6656e125..662685ed 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "SparseMatrixColorings"
 uuid = "0a514795-09f3-496d-8182-132a7b665d35"
 authors = ["Guillaume Dalle", "Alexis Montoison"]
-version = "0.4.21"
+version = "0.4.22"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -12,17 +12,25 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [weakdeps]
+BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+BlockArrays = "8e7c35d0-a365-5155-bbbb-fb81a777f24e"
+BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 CliqueTrees = "60701a23-6482-424a-84db-faee86b9b1f8"
 Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
 
 [extensions]
+SparseMatrixColoringsBandedMatricesExt = "BandedMatrices"
+SparseMatrixColoringsBlockBandedMatricesExt = ["BlockArrays", "BlockBandedMatrices"]
 SparseMatrixColoringsCUDAExt = "CUDA"
 SparseMatrixColoringsCliqueTreesExt = "CliqueTrees"
 SparseMatrixColoringsColorsExt = "Colors"
 
 [compat]
 ADTypes = "1.2.1"
+BandedMatrices = "1.9.4"
+BlockArrays = "1.6.3"
+BlockBandedMatrices = "0.13.1"
 CUDA = "5.8.2"
 CliqueTrees = "1"
 Colors = "0.12.11, 0.13"
diff --git a/docs/make.jl b/docs/make.jl
index 78fba268..46536a16 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -2,7 +2,10 @@ using Documenter
 using DocumenterInterLinks
 using SparseMatrixColorings
 
-links = InterLinks("ADTypes" => "https://sciml.github.io/ADTypes.jl/stable/")
+links = InterLinks(
+    "ADTypes" => "https://sciml.github.io/ADTypes.jl/stable/",
+    "BandedMatrices" => "https://julialinearalgebra.github.io/BandedMatrices.jl/stable/",
+)
 
 cp(joinpath(@__DIR__, "..", "README.md"), joinpath(@__DIR__, "src", "index.md"); force=true)
 
diff --git a/docs/src/api.md b/docs/src/api.md
index c121d1e3..4fd6d28e 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -17,8 +17,14 @@ SparseMatrixColorings
 coloring
 fast_coloring
 ColoringProblem
+```
+
+## Coloring algorithms
+
+```@docs
 GreedyColoringAlgorithm
 ConstantColoringAlgorithm
+StructuredColoringAlgorithm
 ```
 
 ## Result analysis
diff --git a/docs/src/dev.md b/docs/src/dev.md
index 2f253dbe..0f2510f4 100644
--- a/docs/src/dev.md
+++ b/docs/src/dev.md
@@ -76,3 +76,9 @@ SparseMatrixColorings.what_fig_61
 SparseMatrixColorings.efficient_fig_1
 SparseMatrixColorings.efficient_fig_4
 ```
+
+## Misc
+
+```@docs
+SparseMatrixColorings.cycle_range
+```
diff --git a/ext/SparseMatrixColoringsBandedMatricesExt.jl b/ext/SparseMatrixColoringsBandedMatricesExt.jl
new file mode 100644
index 00000000..05d9677c
--- /dev/null
+++ b/ext/SparseMatrixColoringsBandedMatricesExt.jl
@@ -0,0 +1,45 @@
+module SparseMatrixColoringsBandedMatricesExt
+
+using BandedMatrices: BandedMatrix, bandrange, bandwidths, colrange, rowrange
+using SparseMatrixColorings:
+    BipartiteGraph,
+    ColoringProblem,
+    ColumnColoringResult,
+    StructuredColoringAlgorithm,
+    RowColoringResult,
+    column_colors,
+    cycle_range,
+    row_colors
+import SparseMatrixColorings as SMC
+
+#=
+This code is partly taken from ArrayInterface.jl and FiniteDiff.jl
+https://github.com/JuliaArrays/ArrayInterface.jl
+https://github.com/JuliaDiff/FiniteDiff.jl
+=#
+
+function SMC.coloring(
+    A::BandedMatrix,
+    ::ColoringProblem{:nonsymmetric,:column},
+    ::StructuredColoringAlgorithm;
+    kwargs...,
+)
+    width = length(bandrange(A))
+    color = cycle_range(width, size(A, 2))
+    bg = BipartiteGraph(A)
+    return ColumnColoringResult(A, bg, color)
+end
+
+function SMC.coloring(
+    A::BandedMatrix,
+    ::ColoringProblem{:nonsymmetric,:row},
+    ::StructuredColoringAlgorithm;
+    kwargs...,
+)
+    width = length(bandrange(A))
+    color = cycle_range(width, size(A, 1))
+    bg = BipartiteGraph(A)
+    return RowColoringResult(A, bg, color)
+end
+
+end
diff --git a/ext/SparseMatrixColoringsBlockBandedMatricesExt.jl b/ext/SparseMatrixColoringsBlockBandedMatricesExt.jl
new file mode 100644
index 00000000..aaecb0ad
--- /dev/null
+++ b/ext/SparseMatrixColoringsBlockBandedMatricesExt.jl
@@ -0,0 +1,97 @@
+module SparseMatrixColoringsBlockBandedMatricesExt
+
+using BlockArrays: blockaxes, blockfirsts, blocklasts, blocksize, blocklengths
+using BlockBandedMatrices:
+    BandedBlockBandedMatrix,
+    BlockBandedMatrix,
+    blockbandrange,
+    blockbandwidths,
+    blocklengths,
+    blocksize,
+    subblockbandwidths
+using SparseMatrixColorings:
+    BipartiteGraph,
+    ColoringProblem,
+    ColumnColoringResult,
+    StructuredColoringAlgorithm,
+    RowColoringResult,
+    column_colors,
+    cycle_range,
+    row_colors
+import SparseMatrixColorings as SMC
+
+#=
+This code is partly taken from ArrayInterface.jl and FiniteDiff.jl
+https://github.com/JuliaArrays/ArrayInterface.jl
+https://github.com/JuliaDiff/FiniteDiff.jl
+=#
+
+function subblockbandrange(A::BandedBlockBandedMatrix)
+    u, l = subblockbandwidths(A)
+    return (-l):u
+end
+
+function blockbanded_coloring(
+    A::Union{BlockBandedMatrix,BandedBlockBandedMatrix}, dim::Integer
+)
+    # consider blocks of columns or rows (let's call them vertices) depending on `dim`
+    nb_blocks = blocksize(A, dim)
+    nb_in_block = blocklengths(axes(A, dim))
+    first_in_block = blockfirsts(axes(A, dim))
+    last_in_block = blocklasts(axes(A, dim))
+    color = zeros(Int, size(A, dim))
+
+    # give a macroscopic color to each block, so that 2 blocks with the same macro color are orthogonal
+    # same idea as for BandedMatrices
+    nb_macrocolors = length(blockbandrange(A))
+    macrocolor = cycle_range(nb_macrocolors, nb_blocks)
+
+    width = if A isa BandedBlockBandedMatrix
+        # vertices within a block are colored cleverly using bands
+        length(subblockbandrange(A))
+    else
+        # vertices within a block are colored naively with distinct micro colors (~ infinite band width)
+        typemax(Int)
+    end
+
+    # for each macroscopic color, count how many microscopic colors will be needed
+    nb_colors_in_macrocolor = zeros(Int, nb_macrocolors)
+    for mc in 1:nb_macrocolors
+        largest_nb_in_macrocolor = maximum(nb_in_block[mc:nb_macrocolors:nb_blocks]; init=0)
+        nb_colors_in_macrocolor[mc] = min(width, largest_nb_in_macrocolor)
+    end
+    color_shift_in_macrocolor = vcat(0, cumsum(nb_colors_in_macrocolor)[1:(end - 1)])
+
+    # assign a microscopic color to each column as a function of its macroscopic color and its position within the block
+    for b in 1:nb_blocks
+        block_color = cycle_range(width, nb_in_block[b])
+        shift = color_shift_in_macrocolor[macrocolor[b]]
+        color[first_in_block[b]:last_in_block[b]] .= shift .+ block_color
+    end
+
+    return color
+end
+
+function SMC.coloring(
+    A::Union{BlockBandedMatrix,BandedBlockBandedMatrix},
+    ::ColoringProblem{:nonsymmetric,:column},
+    ::StructuredColoringAlgorithm;
+    kwargs...,
+)
+    color = blockbanded_coloring(A, 2)
+    bg = BipartiteGraph(A)
+    return ColumnColoringResult(A, bg, color)
+end
+
+function SMC.coloring(
+    A::Union{BlockBandedMatrix,BandedBlockBandedMatrix},
+    ::ColoringProblem{:nonsymmetric,:row},
+    ::StructuredColoringAlgorithm;
+    kwargs...,
+)
+    color = blockbanded_coloring(A, 1)
+    bg = BipartiteGraph(A)
+    return RowColoringResult(A, bg, color)
+end
+
+end
diff --git a/src/SparseMatrixColorings.jl b/src/SparseMatrixColorings.jl
index 7c25bac4..532ef192 100644
--- a/src/SparseMatrixColorings.jl
+++ b/src/SparseMatrixColorings.jl
@@ -14,11 +14,13 @@ using Base.Iterators: Iterators
 using DocStringExtensions: README, EXPORTS, SIGNATURES, TYPEDEF, TYPEDFIELDS
 using LinearAlgebra:
     Adjoint,
+    Bidiagonal,
     Diagonal,
     Hermitian,
     LowerTriangular,
     Symmetric,
     Transpose,
+    Tridiagonal,
     UpperTriangular,
     adjoint,
     checksquare,
@@ -53,6 +55,7 @@ include("interface.jl")
 include("constant.jl")
 include("adtypes.jl")
 include("decompression.jl")
+include("structured.jl")
 include("check.jl")
 include("examples.jl")
 include("show_colors.jl")
@@ -63,7 +66,7 @@ export NaturalOrder, RandomOrder, LargestFirst
 export DynamicDegreeBasedOrder, SmallestLast, IncidenceDegree, DynamicLargestFirst
 export PerfectEliminationOrder
 export ColoringProblem, GreedyColoringAlgorithm, AbstractColoringResult
-export ConstantColoringAlgorithm
+export ConstantColoringAlgorithm, StructuredColoringAlgorithm
 export coloring, fast_coloring
 export column_colors, row_colors, ncolors
 export column_groups, row_groups
diff --git a/src/structured.jl b/src/structured.jl
new file mode 100644
index 00000000..812256bf
--- /dev/null
+++ b/src/structured.jl
@@ -0,0 +1,181 @@
+"""
+    StructuredColoringAlgorithm  <: ADTypes.AbstractColoringAlgorithm
+
+Coloring algorithm which leverages specific matrix structures to produce optimal or near-optimal solutions.
+
+The following matrix types are supported:
+
+- From the standard library `LinearAlgebra`: `Diagonal`, `Bidiagonal`, `Tridiagonal`
+- From [BandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BandedMatrices.jl): [`BandedMatrix`](@extref BandedMatrices.BandedMatrix)
+
+!!! warning
+    Only `:nonsymmetric` structures with `:row` or `:column` partitions (aka unidirectional Jacobian colorings) are supported by this algorithm at the moment.
+
+!!! tip
+    To request support for a new type of structured matrix, open an issue on the SparseMatrixColorings.jl GitHub repository!
+"""
+struct StructuredColoringAlgorithm <: ADTypes.AbstractColoringAlgorithm end
+
+#=
+This code is partly taken from ArrayInterface.jl
+https://github.com/JuliaArrays/ArrayInterface.jl
+=#
+
+"""
+    cycle_range(k::Integer, n::Integer)
+
+Concatenate copies of `1:k` to fill a vector of length `n` (with one partial copy allowed at the end).
+"""
+function cycle_range(k::Integer, n::Integer)
+    color = Vector{Int}(undef, n)
+    for i in eachindex(color)
+        color[i] = 1 + (i - 1) % k
+    end
+    return color
+end
+
+## Diagonal
+
+function coloring(
+    A::Diagonal,
+    ::ColoringProblem{:nonsymmetric,:column},
+    ::StructuredColoringAlgorithm;
+    kwargs...,
+)
+    color = fill(1, size(A, 2))
+    bg = BipartiteGraph(A)
+    return ColumnColoringResult(A, bg, color)
+end
+
+function coloring(
+    A::Diagonal,
+    ::ColoringProblem{:nonsymmetric,:row},
+    ::StructuredColoringAlgorithm;
+    kwargs...,
+)
+    color = fill(1, size(A, 1))
+    bg = BipartiteGraph(A)
+    return RowColoringResult(A, bg, color)
+end
+
+function decompress!(A::Diagonal, B::AbstractMatrix, result::ColumnColoringResult)
+    color = column_colors(result)
+    for j in axes(A, 2)
+        A[j, j] = B[j, color[j]]
+    end
+    return A
+end
+
+function decompress!(A::Diagonal, B::AbstractMatrix, result::RowColoringResult)
+    color = row_colors(result)
+    for i in axes(A, 1)
+        A[i, i] = B[color[i], i]
+    end
+    return A
+end
+
+## Bidiagonal
+
+function coloring(
+    A::Bidiagonal,
+    ::ColoringProblem{:nonsymmetric,:column},
+    ::StructuredColoringAlgorithm;
+    kwargs...,
+)
+    color = cycle_range(2, size(A, 2))
+    bg = BipartiteGraph(A)
+    return ColumnColoringResult(A, bg, color)
+end
+
+function coloring(
+    A::Bidiagonal,
+    ::ColoringProblem{:nonsymmetric,:row},
+    ::StructuredColoringAlgorithm;
+    kwargs...,
+)
+    color = cycle_range(2, size(A, 1))
+    bg = BipartiteGraph(A)
+    return RowColoringResult(A, bg, color)
+end
+
+function decompress!(A::Bidiagonal, B::AbstractMatrix, result::ColumnColoringResult)
+    color = column_colors(result)
+    for j in axes(A, 2)
+        c = color[j]
+        A[j, j] = B[j, c]
+        if A.uplo == 'U' && j > 1  # above
+            A[j - 1, j] = B[j - 1, c]
+        elseif A.uplo == 'L' && j < size(A, 2)  # below
+            A[j + 1, j] = B[j + 1, c]
+        end
+    end
+    return A
+end
+
+function decompress!(A::Bidiagonal, B::AbstractMatrix, result::RowColoringResult)
+    color = row_colors(result)
+    for i in axes(A, 1)
+        c = color[i]
+        A[i, i] = B[c, i]
+        if A.uplo == 'U' && i < size(A, 1)  # right
+            A[i, i + 1] = B[c, i + 1]
+        elseif A.uplo == 'L' && i > 1  # left
+            A[i, i - 1] = B[c, i - 1]
+        end
+    end
+    return A
+end
+
+## Tridiagonal
+
+function coloring(
+    A::Tridiagonal,
+    ::ColoringProblem{:nonsymmetric,:column},
+    ::StructuredColoringAlgorithm;
+    kwargs...,
+)
+    color = cycle_range(3, size(A, 2))
+    bg = BipartiteGraph(A)
+    return ColumnColoringResult(A, bg, color)
+end
+
+function coloring(
+    A::Tridiagonal,
+    ::ColoringProblem{:nonsymmetric,:row},
+    ::StructuredColoringAlgorithm;
+    kwargs...,
+)
+    color = cycle_range(3, size(A, 1))
+    bg = BipartiteGraph(A)
+    return RowColoringResult(A, bg, color)
+end
+
+function decompress!(A::Tridiagonal, B::AbstractMatrix, result::ColumnColoringResult)
+    color = column_colors(result)
+    for j in axes(A, 2)
+        c = color[j]
+        A[j, j] = B[j, c]
+        if j > 1  # above
+            A[j - 1, j] = B[j - 1, c]
+        end
+        if j < size(A, 2)  # below
+            A[j + 1, j] = B[j + 1, c]
+        end
+    end
+    return A
+end
+
+function decompress!(A::Tridiagonal, B::AbstractMatrix, result::RowColoringResult)
+    color = row_colors(result)
+    for i in axes(A, 1)
+        c = color[i]
+        A[i, i] = B[c, i]
+        if i < size(A, 1)  # right
+            A[i, i + 1] = B[c, i + 1]
+        end
+        if i > 1  # left
+            A[i, i - 1] = B[c, i - 1]
+        end
+    end
+    return A
+end
diff --git a/test/structured.jl b/test/structured.jl
index 23ba967f..d61c7735 100644
--- a/test/structured.jl
+++ b/test/structured.jl
@@ -6,53 +6,65 @@ using SparseMatrixColorings
 using Test
 
 @testset "Diagonal" begin
-    for n in (1, 2, 10, 100)
-        A = Diagonal(rand(n))
-        test_structured_coloring_decompression(A)
+    @testset for algo in [GreedyColoringAlgorithm(), StructuredColoringAlgorithm()]
+        for n in (1, 2, 10, 100)
+            A = Diagonal(rand(n))
+            test_structured_coloring_decompression(A, algo)
+        end
     end
 end;
 
 @testset "Bidiagonal" begin
-    for n in (2, 10, 100)
-        A1 = Bidiagonal(rand(n), rand(n - 1), :U)
-        A2 = Bidiagonal(rand(n), rand(n - 1), :L)
-        test_structured_coloring_decompression(A1)
-        test_structured_coloring_decompression(A2)
+    @testset for algo in [GreedyColoringAlgorithm(), StructuredColoringAlgorithm()]
+        for n in (2, 10, 100)
+            A1 = Bidiagonal(rand(n), rand(n - 1), :U)
+            A2 = Bidiagonal(rand(n), rand(n - 1), :L)
+            test_structured_coloring_decompression(A1, algo)
+            test_structured_coloring_decompression(A2, algo)
+        end
     end
 end;
 
 @testset "Tridiagonal" begin
-    for n in (2, 10, 100)
-        A = Tridiagonal(rand(n - 1), rand(n), rand(n - 1))
-        test_structured_coloring_decompression(A)
+    @testset for algo in [GreedyColoringAlgorithm(), StructuredColoringAlgorithm()]
+        for n in (2, 10, 100)
+            A = Tridiagonal(rand(n - 1), rand(n), rand(n - 1))
+            test_structured_coloring_decompression(A, algo)
+        end
     end
 end;
 
 @testset "BandedMatrices" begin
-    @testset for (m, n) in [(10, 20), (20, 10)], l in 0:5, u in 0:5
-        A = brand(m, n, l, u)
-        test_structured_coloring_decompression(A)
+    @testset for algo in [GreedyColoringAlgorithm(), StructuredColoringAlgorithm()]
+        @testset for (m, n) in [(10, 20), (20, 10)], l in 0:5, u in 0:5
+            A = brand(m, n, l, u)
+            test_structured_coloring_decompression(A, algo)
+        end
     end
 end;
 
 @testset "BlockBandedMatrices" begin
-    for (mb, nb) in [(10, 20), (20, 10)], lb in 0:3, ub in 0:3, _ in 1:10
-        rows = rand(1:5, mb)
-        cols = rand(1:5, nb)
-        A = BlockBandedMatrix{Float64}(rand(sum(rows), sum(cols)), rows, cols, (lb, ub))
-        test_structured_coloring_decompression(A)
+    @testset for algo in [GreedyColoringAlgorithm(), StructuredColoringAlgorithm()]
+        for (mb, nb) in [(10, 20), (20, 10)], lb in 0:3, ub in 0:3, _ in 1:10
+            rows = rand(1:5, mb)
+            cols = rand(1:5, nb)
+            A = BlockBandedMatrix{Float64}(rand(sum(rows), sum(cols)), rows, cols, (lb, ub))
+            test_structured_coloring_decompression(A, algo)
+        end
     end
 end;
 
 @testset "BandedBlockBandedMatrices" begin
-    for (mb, nb) in [(10, 20), (20, 10)], lb in 0:3, ub in 0:3, _ in 1:10
-        rows = rand(5:10, mb)
-        cols = rand(5:10, nb)
-        λ = rand(0:5)
-        μ = rand(0:5)
-        A = BandedBlockBandedMatrix{Float64}(
-            rand(sum(rows), sum(cols)), rows, cols, (lb, ub), (λ, μ)
-        )
-        test_structured_coloring_decompression(A)
+    @testset for algo in [GreedyColoringAlgorithm(), StructuredColoringAlgorithm()]
+        for (mb, nb) in [(10, 20), (20, 10)], lb in 0:3, ub in 0:3, _ in 1:10
+            rows = rand(5:10, mb)
+            cols = rand(5:10, nb)
+            λ = rand(0:5)
+            μ = rand(0:5)
+            A = BandedBlockBandedMatrix{Float64}(
+                rand(sum(rows), sum(cols)), rows, cols, (lb, ub), (λ, μ)
+            )
+            test_structured_coloring_decompression(A, algo)
+        end
     end
 end;
diff --git a/test/utils.jl b/test/utils.jl
index bb80f95f..200d07d5 100644
--- a/test/utils.jl
+++ b/test/utils.jl
@@ -218,10 +218,11 @@ function test_bicoloring_decompression(
     end
 end
 
-function test_structured_coloring_decompression(A::AbstractMatrix)
+function test_structured_coloring_decompression(
+    A::AbstractMatrix, algo=StructuredColoringAlgorithm()
+)
     column_problem = ColoringProblem(; structure=:nonsymmetric, partition=:column)
     row_problem = ColoringProblem(; structure=:nonsymmetric, partition=:row)
-    algo = GreedyColoringAlgorithm()
 
     # Column
     result = coloring(A, column_problem, algo)
@@ -231,9 +232,8 @@ function test_structured_coloring_decompression(A::AbstractMatrix)
     @test D == A
     @test nameof(typeof(D)) == nameof(typeof(A))
     @test structurally_orthogonal_columns(A, color)
-    if VERSION >= v"1.10" || A isa Union{Diagonal,Bidiagonal,Tridiagonal}
-        # banded matrices not supported by ArrayInterface on Julia 1.6
-        # @test color == ArrayInterface.matrix_colors(A)  # TODO: uncomment
+    if algo isa StructuredColoringAlgorithm
+        @test color == ArrayInterface.matrix_colors(A)
     end
 
     # Row