Edge coloring (#98)

Co-authored-by: Matt Fishman <[email protected]>

Author: JoeyT1994

Project.toml

@@ -1,7 +1,7 @@
 name = "NamedGraphs"
 uuid = "678767b0-92e7-4007-89e4-4527a8725b19"
 authors = ["Matthew Fishman <[email protected]>, Joseph Tindall <[email protected]> and contributors"]
-version = "0.6.7"
+version = "0.6.8"
 
 [deps]
 AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
@@ -11,6 +11,8 @@ Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 PackageExtensionCompat = "65ce6f38-6b18-4e1d-a461-8949797d7930"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+SimpleGraphAlgorithms = "41400c72-0c58-5c16-8579-4ecbce768449"
+SimpleGraphConverter = "205b04f2-f585-4877-a239-566270b3f673"
 SimpleTraits = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SplitApplyCombine = "03a91e81-4c3e-53e1-a0a4-9c0c8f19dd66"
@@ -26,6 +28,7 @@ SymRCM = "286e6d88-80af-4590-acc9-0001b223b9bd"
 NamedGraphsGraphsFlowsExt = "GraphsFlows"
 NamedGraphsKaHyParExt = "KaHyPar"
 NamedGraphsMetisExt = "Metis"
+NamedGraphsSimpleGraphAlgorithmsExt = "SimpleGraphAlgorithms"
 NamedGraphsSymRCMExt = "SymRCM"
 
 [compat]
@@ -38,6 +41,8 @@ KaHyPar = "0.3.1"
 LinearAlgebra = "1.7"
 Metis = "1.4"
 PackageExtensionCompat = "1"
+SimpleGraphAlgorithms = "0.6.0"
+SimpleGraphConverter = "0.1.0"
 SimpleTraits = "0.9"
 SparseArrays = "1.7"
 SplitApplyCombine = "1.2.2"
@@ -49,6 +54,8 @@ julia = "1.7"
 GraphsFlows = "06909019-6f44-4949-96fc-b9d9aaa02889"
 KaHyPar = "2a6221f6-aa48-11e9-3542-2d9e0ef01880"
 Metis = "2679e427-3c69-5b7f-982b-ece356f1e94b"
+SimpleGraphAlgorithms = "41400c72-0c58-5c16-8579-4ecbce768449"
+SimpleGraphConverter = "205b04f2-f585-4877-a239-566270b3f673"
 SymRCM = "286e6d88-80af-4590-acc9-0001b223b9bd"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 

ext/NamedGraphsSimpleGraphAlgorithmsExt/NamedGraphsSimpleGraphAlgorithmsExt.jl

@@ -0,0 +1,17 @@
+module NamedGraphsSimpleGraphAlgorithmsExt
+using Graphs: edgetype
+using NamedGraphs: AbstractNamedGraph, position_graph, vertices
+using NamedGraphs.GraphsExtensions: GraphsExtensions
+using SimpleGraphAlgorithms: SimpleGraphAlgorithms
+using SimpleGraphConverter: UndirectedGraph
+
+function SimpleGraphAlgorithms.edge_color(g::AbstractNamedGraph, k::Int64)
+  pg, vs = position_graph(g), collect(vertices(g))
+  ec_dict = SimpleGraphAlgorithms.edge_color(UndirectedGraph(pg), k)
+  # returns k vectors of edges which each contain the colored/commuting edges
+  return [
+    [edgetype(g)(vs[first(first(e))], vs[last(first(e))]) for e in ec_dict if last(e) == i]
+    for i in 1:k
+  ]
+end
+end

test/Project.toml

@@ -9,6 +9,8 @@ Metis = "2679e427-3c69-5b7f-982b-ece356f1e94b"
 NamedGraphs = "678767b0-92e7-4007-89e4-4527a8725b19"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+SimpleGraphAlgorithms = "41400c72-0c58-5c16-8579-4ecbce768449"
+SimpleGraphConverter = "205b04f2-f585-4877-a239-566270b3f673"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
 SymRCM = "286e6d88-80af-4590-acc9-0001b223b9bd"
@@ -24,6 +26,8 @@ KaHyPar = "0.3.1"
 Metis = "1.5.0"
 NamedGraphs = "0.6.6"
 SafeTestsets = "0.1.0"
+SimpleGraphAlgorithms = "0.6.0"
+SimpleGraphConverter = "0.1.0"
 Suppressor = "0.2.8"
 SymRCM = "0.2.2"
 Pkg = "1.10.0"

test/test_edge_coloring.jl

@@ -0,0 +1,25 @@
+@eval module $(gensym())
+using Graphs: degree, dst, edges, ne, src, vertices
+using NamedGraphs.NamedGraphGenerators:
+  named_comb_tree, named_grid, named_hexagonal_lattice_graph
+using SimpleGraphConverter
+using SimpleGraphAlgorithms: edge_color
+using Test: @test, @testset
+
+@testset "EdgeColoring" begin
+  g = named_grid((4, 4); periodic=true)
+
+  #For bipartite graphs, a coloring can always be achieved, in linear time,
+  #using the maximum degree of the graph
+  k = maximum([degree(g, v) for v in vertices(g)])
+  colored_edges = edge_color(g, k)
+  #Test all edges are present in the coloring
+  @test issetequal(reduce(vcat, colored_edges), edges(g))
+  #Test all colors have same number of edges in this case
+  @test all([length(es) == ne(g) / k for es in colored_edges])
+  #Test every vertex appears only once in each group (no overlapping edges in the coloring)
+  @test all([
+    unique(vcat(src.(es), dst.(es))) == vcat(src.(es), dst.(es)) for es in colored_edges
+  ])
+end
+end