Add rectangle example (#177)

* Add rectangle example

* Add arrowhead

* Remove comment

* Add triangle

Author: gdalle

test/small.jl

@@ -8,6 +8,7 @@ using SparseMatrixColorings:
     what_fig_61,
     efficient_fig_1,
     efficient_fig_4
+using StableRNGs
 using Test
 
 @testset "Column coloring & decompression" begin
@@ -85,3 +86,75 @@ end;
         test_coloring_decompression(A0, problem, algo; B0, color0)
     end
 end;
+
+@testset "Bidirectional coloring" begin
+    problem = ColoringProblem(; structure=:nonsymmetric, partition=:bidirectional)
+    order = RandomOrder(StableRNG(0), 0)
+
+    @testset "Triangle" begin
+        A = sparse([1 1 0; 0 1 1; 1 0 1])
+
+        result = coloring(
+            A, problem, GreedyColoringAlgorithm{:direct}(; postprocessing=true)
+        )
+        @test ncolors(result) == 3
+
+        result = coloring(
+            A, problem, GreedyColoringAlgorithm{:substitution}(; postprocessing=true)
+        )
+        @test ncolors(result) == 3
+    end
+
+    @testset "Rectangle" begin
+        A = spzeros(Bool, 10, 20)
+        A[:, 1] .= 1
+        A[:, end] .= 1
+        A[1, :] .= 1
+        A[end, :] .= 1
+
+        result = coloring(
+            A, problem, GreedyColoringAlgorithm{:direct}(order; postprocessing=false)
+        )
+        @test ncolors(result) == 6  # two more than necessary
+        result = coloring(
+            A, problem, GreedyColoringAlgorithm{:direct}(order; postprocessing=true)
+        )
+        @test ncolors(result) == 4  # optimal number
+
+        result = coloring(
+            A, problem, GreedyColoringAlgorithm{:substitution}(order; postprocessing=false)
+        )
+        @test ncolors(result) == 6  # two more than necessary
+        result = coloring(
+            A, problem, GreedyColoringAlgorithm{:substitution}(order; postprocessing=true)
+        )
+        @test ncolors(result) == 4  # optimal number
+    end
+
+    @testset "Arrowhead" begin
+        A = spzeros(Bool, 10, 10)
+        for i in axes(A, 1)
+            A[1, i] = 1
+            A[i, 1] = 1
+            A[i, i] = 1
+        end
+
+        result = coloring(
+            A, problem, GreedyColoringAlgorithm{:direct}(order; postprocessing=true)
+        )
+        @test ncolors(coloring(A, problem, GreedyColoringAlgorithm{:substitution}(order))) <
+            ncolors(coloring(A, problem, GreedyColoringAlgorithm{:direct}(order)))
+
+        @test ncolors(
+            coloring(
+                A,
+                problem,
+                GreedyColoringAlgorithm{:substitution}(order; postprocessing=true),
+            ),
+        ) < ncolors(
+            coloring(
+                A, problem, GreedyColoringAlgorithm{:direct}(order; postprocessing=true)
+            ),
+        )
+    end
+end