initial benchmarks on n nodes with 2 bags

benchmarks/GraphColoring.jl

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+# This file benchmarks the StructuredDecompositions method of graph coloring
+
+# RESULTS = sheaf tree skeletal coloring is n linear for false returns, worse than n exponential for true returns
+    # shouldn't be worse than exponential for true returns so I will take a look at it after considering k
+
+import Graphs as GraphsPkg
+
+using BenchmarkTools
+using PkgBenchmark
+
+using StructuredDecompositions.Decompositions
+using StructuredDecompositions.DecidingSheaves
+using StructuredDecompositions.FunctorUtils
+
+using Catlab.Graphs
+using Catlab.ACSetInterface
+using Catlab.CategoricalAlgebra
+using Catlab.Graphics
+
+# The following structures and functions were pulled from DecidingSheaves.jl 
+
+struct Coloring
+    n     
+    func
+end
+
+K(n) = complete_graph(Graph, n)
+Coloring(n) = Coloring(n, g -> homomorphisms(g, K(n) ))
+(c::Coloring)(X::Graph) = FinSet(c.func(X))
+function (c::Coloring)(f::ACSetTransformation)  
+    (G₁, G₂)   = (dom(f), codom(f)) 
+    (cG₁, cG₂) = (c(G₁), c(G₂))
+    FinFunction( λ₂ -> compose(f,λ₂), cG₂, cG₁ )
+end
+
+skeletalColoring(n) = skeleton ∘ Coloring(n)
+
+colorability_test(n, the_test_case) = is_homomorphic(ob(colimit(the_test_case)), K(n)) == decide_sheaf_tree_shape(skeletalColoring(n), the_test_case)[1]
+
+
+# Benchmark 1 (small n per bag(4) and small bags k(2), 3 coloring)
+
+#bag 1
+H₁ = @acset Graph begin
+  V = 4
+  E = 4
+  src = [1, 2, 3, 4]
+  tgt = [2, 3, 4, 1]
+end
+
+#adhesion 1,2
+H₁₂ = @acset Graph begin
+  V = 2
+end
+
+#bag 2
+H₂ = @acset Graph begin
+  V = 4
+  E = 5
+  src = [1, 2, 3, 4, 1]
+  tgt = [2, 3, 4, 1, 3]
+end
+
+Gₛ = @acset Graph begin
+  V = 2
+  E = 1
+  src = [1]
+  tgt = [2]
+end
+
+#transformations
+Γₛ⁰ = Dict(1 => H₁, 2 => H₂, 3 => H₁₂)
+Γₛ = FinDomFunctor(
+  Γₛ⁰,
+  Dict(
+   1 => ACSetTransformation(Γₛ⁰[3], Γₛ⁰[1], V=[1, 3]),
+   2 => ACSetTransformation(Γₛ⁰[3], Γₛ⁰[2], V=[2, 1]),
+ ),
+ ∫(Gₛ)
+)
+
+my_decomp1  = StrDecomp(Gₛ, Γₛ)
+
+is_homomorphic(ob(colimit(my_decomp1)), K(2)) == false
+@benchmark is_homomorphic(ob(colimit(my_decomp1)), K(2))
+
+is_homomorphic(ob(colimit(my_decomp1)), K(3)) == true
+@benchmark is_homomorphic(ob(colimit(my_decomp1)), K(3))
+
+is_homomorphic(ob(colimit(my_decomp1)), K(4)) == true
+@benchmark is_homomorphic(ob(colimit(my_decomp1)), K(4))
+
+decide_sheaf_tree_shape(skeletalColoring(2), my_decomp1)[1] == false
+@benchmark decide_sheaf_tree_shape(skeletalColoring(2), my_decomp1)[1]
+
+decide_sheaf_tree_shape(skeletalColoring(3), my_decomp1)[1] == true
+@benchmark decide_sheaf_tree_shape(skeletalColoring(3), my_decomp1)[1]
+
+decide_sheaf_tree_shape(skeletalColoring(4), my_decomp1)[1] == true
+@benchmark decide_sheaf_tree_shape(skeletalColoring(4), my_decomp1)[1]
+
+
+# Benchmark 2 (medium n per bag(10) and small bags k(2), 3 coloring)
+
+#bag 1
+H₁ = @acset Graph begin
+  V = 10
+  E = 16
+  src = [1, 1, 1, 2, 2, 3, 4, 4, 4, 6, 6, 7, 7, 7, 8, 9]
+  tgt = [2, 5, 6, 3, 8, 4, 5, 9, 10, 7, 10, 8, 9, 10, 9, 10]
+end
+
+#adhesion 1,2
+H₁₂ = @acset Graph begin
+  V = 2
+end
+
+#bag 2
+H₂ = @acset Graph begin
+  V = 10
+  E = 18
+  src = [1, 1, 2, 2, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 9]
+  tgt = [2, 9, 3, 4, 9, 10, 4, 5, 10, 6, 10, 7, 10, 8, 9, 10, 9, 10]
+end
+
+Gₛ = @acset Graph begin
+  V = 2
+  E = 1
+  src = [1]
+  tgt = [2]
+end
+
+#transformations
+Γₛ⁰ = Dict(1 => H₁, 2 => H₂, 3 => H₁₂)
+Γₛ = FinDomFunctor(
+  Γₛ⁰,
+  Dict(
+    1 => ACSetTransformation(Γₛ⁰[3], Γₛ⁰[1], V=[4, 2]),
+    2 => ACSetTransformation(Γₛ⁰[3], Γₛ⁰[2], V=[1, 3]),
+  ),
+  ∫(Gₛ)
+)
+
+my_decomp2  = StrDecomp(Gₛ, Γₛ)
+
+is_homomorphic(ob(colimit(my_decomp2)), K(2)) == false
+@benchmark is_homomorphic(ob(colimit(my_decomp2)), K(2))
+
+is_homomorphic(ob(colimit(my_decomp2)), K(3)) == true
+@benchmark is_homomorphic(ob(colimit(my_decomp2)), K(3))
+
+is_homomorphic(ob(colimit(my_decomp2)), K(4)) == true
+@benchmark is_homomorphic(ob(colimit(my_decomp2)), K(4))
+
+decide_sheaf_tree_shape(skeletalColoring(2), my_decomp2)[1] == false
+@benchmark decide_sheaf_tree_shape(skeletalColoring(2), my_decomp2)[1]
+
+decide_sheaf_tree_shape(skeletalColoring(3), my_decomp2)[1] == true
+@benchmark decide_sheaf_tree_shape(skeletalColoring(3), my_decomp2)[1]
+
+decide_sheaf_tree_shape(skeletalColoring(4), my_decomp2)[1] == true
+@benchmark decide_sheaf_tree_shape(skeletalColoring(4), my_decomp2)[1]
+
+
+# Benchmark 3 (large n per bag(20) and small bags k(2), 3 coloring)
+
+#bag 1
+H₁ = @acset Graph begin
+  V = 20
+  E = 34
+  src = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18]
+  tgt = [2, 3, 4, 5, 4, 6, 5, 7, 8, 9, 7, 10, 8, 11, 9, 12, 13, 14, 11, 15, 12, 15, 13, 16, 14, 17, 18, 16, 19, 17, 19, 18, 19, 20]
+end
+
+#adhesion 1,2
+H₁₂ = @acset Graph begin
+  V = 2
+end
+
+#bag 2
+H₂ = @acset Graph begin
+  V = 20
+  E = 34
+  src = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18]
+  tgt = [2, 3, 4, 5, 4, 6, 5, 7, 8, 9, 7, 10, 8, 11, 9, 12, 13, 14, 11, 15, 12, 15, 13, 16, 14, 17, 18, 16, 19, 17, 19, 18, 19, 20]
+end
+
+Gₛ = @acset Graph begin
+  V = 2
+  E = 1
+  src = [1]
+  tgt = [2]
+end
+
+#transformations
+Γₛ⁰ = Dict(1 => H₁, 2 => H₂, 3 => H₁₂)
+Γₛ = FinDomFunctor(
+  Γₛ⁰,
+  Dict(
+    1 => ACSetTransformation(Γₛ⁰[3], Γₛ⁰[1], V=[1, 2]),
+    2 => ACSetTransformation(Γₛ⁰[3], Γₛ⁰[2], V=[1, 2]),
+  ),
+  ∫(Gₛ)
+)
+
+my_decomp3  = StrDecomp(Gₛ, Γₛ)
+
+is_homomorphic(ob(colimit(my_decomp3)), K(2)) == false
+@benchmark is_homomorphic(ob(colimit(my_decomp3)), K(2))
+
+is_homomorphic(ob(colimit(my_decomp3)), K(3)) == true
+@benchmark is_homomorphic(ob(colimit(my_decomp3)), K(3))
+
+is_homomorphic(ob(colimit(my_decomp3)), K(4)) == true
+@benchmark is_homomorphic(ob(colimit(my_decomp3)), K(4))
+
+decide_sheaf_tree_shape(skeletalColoring(2), my_decomp3)[1] == false
+@benchmark decide_sheaf_tree_shape(skeletalColoring(2), my_decomp3)[1]
+
+decide_sheaf_tree_shape(skeletalColoring(3), my_decomp3)[1] == true
+@benchmark decide_sheaf_tree_shape(skeletalColoring(3), my_decomp3)[1]
+
+decide_sheaf_tree_shape(skeletalColoring(4), my_decomp3)[1] == true
+@benchmark decide_sheaf_tree_shape(skeletalColoring(4), my_decomp3)[1]
+
+
+# Benchmark 1-3 minimum and median homomorphic comparisons
+
+# all of these are returning false
+min_2_test_1_h = minimum(@benchmark is_homomorphic(ob(colimit(my_decomp1)), K(2)))
+min_2_test_2_h = minimum(@benchmark is_homomorphic(ob(colimit(my_decomp2)), K(2)))
+min_2_test_3_h = minimum(@benchmark is_homomorphic(ob(colimit(my_decomp3)), K(2)))
+ratio(min_2_test_2_h, min_2_test_1_h)
+ratio(min_2_test_3_h, min_2_test_2_h)
+ratio(min_2_test_3_h, min_2_test_1_h)
+
+med_2_test_1_h = median(@benchmark is_homomorphic(ob(colimit(my_decomp1)), K(2)))
+med_2_test_2_h = median(@benchmark is_homomorphic(ob(colimit(my_decomp2)), K(2)))
+med_2_test_3_h = median(@benchmark is_homomorphic(ob(colimit(my_decomp3)), K(2)))
+ratio(med_2_test_2_h, med_2_test_1_h)
+ratio(med_2_test_3_h, med_2_test_2_h)
+ratio(med_2_test_3_h, med_2_test_1_h)
+
+# all of these are returning true
+min_3_test_1_h = minimum(@benchmark is_homomorphic(ob(colimit(my_decomp1)), K(3)))
+min_3_test_2_h = minimum(@benchmark is_homomorphic(ob(colimit(my_decomp2)), K(3)))
+min_3_test_3_h = minimum(@benchmark is_homomorphic(ob(colimit(my_decomp3)), K(3)))
+ratio(min_3_test_2_h, min_3_test_1_h)
+ratio(min_3_test_3_h, min_3_test_2_h)
+ratio(min_3_test_3_h, min_3_test_1_h)
+
+med_3_test_1_h = median(@benchmark is_homomorphic(ob(colimit(my_decomp1)), K(3)))
+med_3_test_2_h = median(@benchmark is_homomorphic(ob(colimit(my_decomp2)), K(3)))
+med_3_test_3_h = median(@benchmark is_homomorphic(ob(colimit(my_decomp3)), K(3)))
+ratio(med_3_test_2_h, med_3_test_1_h)
+ratio(med_3_test_3_h, med_3_test_2_h)
+ratio(med_3_test_3_h, med_3_test_1_h)
+
+# all of these are returning true
+min_4_test_1_h = minimum(@benchmark is_homomorphic(ob(colimit(my_decomp1)), K(4)))
+min_4_test_2_h = minimum(@benchmark is_homomorphic(ob(colimit(my_decomp2)), K(4)))
+min_4_test_3_h = minimum(@benchmark is_homomorphic(ob(colimit(my_decomp3)), K(4)))
+ratio(min_4_test_2_h, min_4_test_1_h)
+ratio(min_4_test_3_h, min_4_test_2_h)
+ratio(min_4_test_3_h, min_4_test_1_h)
+
+med_4_test_1_h = median(@benchmark is_homomorphic(ob(colimit(my_decomp1)), K(4)))
+med_4_test_2_h = median(@benchmark is_homomorphic(ob(colimit(my_decomp2)), K(4)))
+med_4_test_3_h = median(@benchmark is_homomorphic(ob(colimit(my_decomp3)), K(4)))
+ratio(med_4_test_2_h, med_4_test_1_h)
+ratio(med_4_test_3_h, med_4_test_2_h)
+ratio(med_4_test_3_h, med_4_test_1_h)
+
+
+# Benchmark 1-3 minimum and median sheaf tree comparisons
+
+# all of these are returning false
+min_2_test_1_s = minimum(@benchmark decide_sheaf_tree_shape(skeletalColoring(2), my_decomp1)[1])
+min_2_test_2_s = minimum(@benchmark decide_sheaf_tree_shape(skeletalColoring(2), my_decomp2)[1])
+min_2_test_3_s = minimum(@benchmark decide_sheaf_tree_shape(skeletalColoring(2), my_decomp3)[1])
+ratio(min_2_test_2_s, min_2_test_1_s)
+ratio(min_2_test_3_s, min_2_test_2_s)
+ratio(min_2_test_3_s, min_2_test_1_s)
+
+med_2_test_1_s = median(@benchmark decide_sheaf_tree_shape(skeletalColoring(2), my_decomp1)[1])
+med_2_test_2_s = median(@benchmark decide_sheaf_tree_shape(skeletalColoring(2), my_decomp2)[1])
+med_2_test_3_s = median(@benchmark decide_sheaf_tree_shape(skeletalColoring(2), my_decomp3)[1])
+ratio(med_2_test_2_s, med_2_test_1_s)
+ratio(med_2_test_3_s, med_2_test_2_s)
+ratio(med_2_test_3_s, med_2_test_1_s)
+
+# all of these are returning true
+min_3_test_1_s = minimum(@benchmark decide_sheaf_tree_shape(skeletalColoring(3), my_decomp1)[1])
+min_3_test_2_s = minimum(@benchmark decide_sheaf_tree_shape(skeletalColoring(3), my_decomp2)[1])
+min_3_test_3_s = minimum(@benchmark decide_sheaf_tree_shape(skeletalColoring(3), my_decomp3)[1])
+ratio(min_3_test_2_s, min_3_test_1_s)
+ratio(min_3_test_3_s, min_3_test_2_s)
+ratio(min_3_test_3_s, min_3_test_1_s)
+
+med_3_test_1_s = median(@benchmark decide_sheaf_tree_shape(skeletalColoring(3), my_decomp1)[1])
+med_3_test_2_s = median(@benchmark decide_sheaf_tree_shape(skeletalColoring(3), my_decomp2)[1])
+med_3_test_3_s = median(@benchmark decide_sheaf_tree_shape(skeletalColoring(3), my_decomp3)[1])
+ratio(med_3_test_2_s, med_3_test_1_s)
+ratio(med_3_test_3_s, med_3_test_2_s)
+ratio(med_3_test_3_s, med_3_test_1_s)
+
+# all of these are returning true
+min_4_test_1_s = minimum(@benchmark decide_sheaf_tree_shape(skeletalColoring(4), my_decomp1)[1])
+min_4_test_2_s = minimum(@benchmark decide_sheaf_tree_shape(skeletalColoring(4), my_decomp2)[1])
+min_4_test_3_s = minimum(@benchmark decide_sheaf_tree_shape(skeletalColoring(4), my_decomp3)[1])
+ratio(min_4_test_2_s, min_4_test_1_s)
+ratio(min_4_test_3_s, min_4_test_2_s)
+ratio(min_4_test_3_s, min_4_test_1_s)
+
+med_4_test_1_s = median(@benchmark decide_sheaf_tree_shape(skeletalColoring(4), my_decomp1)[1])
+med_4_test_2_s = median(@benchmark decide_sheaf_tree_shape(skeletalColoring(4), my_decomp2)[1])
+med_4_test_3_s = median(@benchmark decide_sheaf_tree_shape(skeletalColoring(4), my_decomp3)[1])
+ratio(med_4_test_2_s, med_4_test_1_s)
+ratio(med_4_test_3_s, med_4_test_2_s)
+ratio(med_4_test_3_s, med_4_test_1_s)
+
+# Benchmark 4 (small n per bag(5) with medium bags k(4), 3 coloring)
+
+# Benchmark 5 (medium n per bag(10) with medium bags k(4), 3 coloring)
+
+# Benchmark 6 (large n per bag(20) with medium bags k(4), 3 coloring)
+
+# Benchmark 7 (small n per bag(5) with large bags k(10), 3 coloring)
+
+# Benchmark 8 (medium n per bag(10) with large bags k(10), 3 coloring)
+
+# Benchmark 9 (large n per bag(20) with large bags k(10), 3 coloring)

benchmarks/Project.toml

@@ -0,0 +1,25 @@
+[deps]
+AMD = "14f7f29c-3bd6-536c-9a0b-7339e30b5a3e"
+AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+Catlab = "134e5e36-593f-5add-ad60-77f754baafbe"
+CuthillMcKee = "17f17636-5e38-52e3-a803-7ae3aaaf3da9"
+DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+MLStyle = "d8e11817-5142-5d16-987a-aa16d5891078"
+Metis = "2679e427-3c69-5b7f-982b-ece356f1e94b"
+PartialFunctions = "570af359-4316-4cb7-8c74-252c00c2016b"
+PkgBenchmark = "32113eaa-f34f-5b0d-bd6c-c81e245fc73d"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
+[compat]
+AbstractTrees = "0.4"
+AMD = "0.5"
+Catlab = "0.16"
+CuthillMcKee = "0.1"
+DataStructures = "0.18"
+MLStyle = "0.4"
+Metis = "1"
+PartialFunctions = "1.1"
+julia = "1.7"

benchmarks/README.md

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+# StructuredDecompositions.jl benchmarks
+
+This directory benchmarks various parts of StructuredDecompositions.jl.