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Added forest cover function #39

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Nov 1, 2023
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1 change: 1 addition & 0 deletions src/NamedGraphs.jl
Original file line number Diff line number Diff line change
Expand Up @@ -113,6 +113,7 @@ include("distance.jl")
include("distances_and_capacities.jl")
include(joinpath("steiner_tree", "steiner_tree.jl"))
include(joinpath("traversals", "dfs.jl"))
include(joinpath("traversals", "trees_and_forests.jl"))
include("namedgraph.jl")
include(joinpath("generators", "named_staticgraphs.jl"))
include(joinpath("Graphs", "generators", "staticgraphs.jl"))
Expand Down
56 changes: 56 additions & 0 deletions src/traversals/trees_and_forests.jl
Original file line number Diff line number Diff line change
@@ -0,0 +1,56 @@
abstract type SpanningTreeAlgorithm end

struct BFS <: SpanningTreeAlgorithm end
struct RandomBFS <: SpanningTreeAlgorithm end
struct DFS <: SpanningTreeAlgorithm end

default_spanning_tree_alg() = BFS()

default_root_vertex(g) = last(findmax(eccentricities(g)))

function spanning_tree(
g::AbstractNamedGraph; alg=default_spanning_tree_alg(), root_vertex=default_root_vertex(g)
)
return spanning_tree(alg, g; root_vertex)
end

@traitfn function spanning_tree(
::BFS, g::AbstractNamedGraph::(!IsDirected); root_vertex=default_root_vertex(g)
)
return undirected_graph(bfs_tree(g, root_vertex))
end

@traitfn function spanning_tree(
::RandomBFS, g::AbstractNamedGraph::(!IsDirected); root_vertex=default_root_vertex(g)
)
return undirected_graph(random_bfs_tree(g, root_vertex))
end

@traitfn function spanning_tree(
::DFS, g::AbstractNamedGraph::(!IsDirected); root_vertex=default_root_vertex(g)
)
return undirected_graph(dfs_tree(g, root_vertex))
end

#Given a graph, split it into its connected components, construct a spanning tree, using the function spanning_tree, over each of them
# and take the union.
function spanning_forest(g::AbstractNamedGraph; spanning_tree=spanning_tree)
return reduce(union, (spanning_tree(g[vs]) for vs in connected_components(g)))
end

#Given an undirected graph g with vertex set V, build a set of forests (each with vertex set V) which covers all edges in g
# (see https://en.wikipedia.org/wiki/Arboricity) We do not find the minimum but our tests show this algorithm performs well
function forest_cover(g::AbstractNamedGraph; spanning_tree=spanning_tree)
edges_collected = edgetype(g)[]
remaining_edges = edges(g)
forests = NamedGraph[]
while !isempty(remaining_edges)
g_reduced = rem_edges(g, edges_collected)
g_reduced_spanning_forest = spanning_forest(g_reduced; spanning_tree)
push!(edges_collected, edges(g_reduced_spanning_forest)...)
push!(forests, g_reduced_spanning_forest)
setdiff!(remaining_edges, edges(g_reduced_spanning_forest))
end

return forests
end
27 changes: 14 additions & 13 deletions test/test_namedgraph.jl
Original file line number Diff line number Diff line change
Expand Up @@ -390,17 +390,16 @@ end
g = NamedGraph(path_graph(4), ["A", "B", "C", "D"])

part1, part2, flow = GraphsFlows.mincut(g, "A", "D")
@test issetequal(part1, ["A"])
@test issetequal(part2, ["B", "C", "D"])
@test "A" ∈ part1
@test "D" ∈ part2
@test flow == 1

part1, part2 = mincut_partitions(g, "A", "D")
@test issetequal(part1, ["A"])
@test issetequal(part2, ["B", "C", "D"])
@test "A" ∈ part1
@test "D" ∈ part2

part1, part2 = mincut_partitions(g)
@test issetequal(part1, ["B", "C", "D"])
@test issetequal(part2, ["A"])
@test issetequal(vcat(part1, part2), vertices(g))

weights_dict = Dict{Tuple{String,String},Float64}()
weights_dict["A", "B"] = 3
Expand All @@ -411,17 +410,17 @@ end

for weights in (weights_dict, weights_dictionary)
part1, part2, flow = GraphsFlows.mincut(g, "A", "D", weights)
@test issetequal(part1, ["A", "B"])
@test issetequal(part2, ["C", "D"])
@test issetequal(part1, ["A", "B"]) || issetequal(part1, ["C", "D"])
@test issetequal(vcat(part1, part2), vertices(g))
@test flow == 2

part1, part2 = mincut_partitions(g, "A", "D", weights)
@test issetequal(part1, ["A", "B"])
@test issetequal(part2, ["C", "D"])
@test issetequal(part1, ["A", "B"]) || issetequal(part1, ["C", "D"])
@test issetequal(vcat(part1, part2), vertices(g))

part1, part2 = mincut_partitions(g, weights)
@test issetequal(part1, ["C", "D"])
@test issetequal(part2, ["A", "B"])
@test issetequal(part1, ["A", "B"]) || issetequal(part1, ["C", "D"])
@test issetequal(vcat(part1, part2), vertices(g))
end
end
@testset "dijkstra" begin
Expand Down Expand Up @@ -557,6 +556,8 @@ end
add_edge!(g, "D" => "G")
add_edge!(g, "E" => "G")
t = topological_sort_by_dfs(g)
@test t == ["C", "B", "E", "A", "D", "G", "F"]
for e in edges(g)
@test findfirst(x -> x == src(e), t) < findfirst(x -> x == dst(e), t)
end
end
end
1 change: 0 additions & 1 deletion test/test_namedgraphgenerators.jl
Original file line number Diff line number Diff line change
Expand Up @@ -30,7 +30,6 @@ using Random
@test dims[1] > dims[2]

g = triangular_lattice_graph(2, 1)
@show g
dims = maximum(vertices(g))
@test dims[1] > dims[2]

Expand Down
38 changes: 38 additions & 0 deletions test/test_trees_and_forests.jl
Original file line number Diff line number Diff line change
@@ -0,0 +1,38 @@
using Test
using Graphs
using NamedGraphs
using NamedGraphs: forest_cover, spanning_tree

module TestTreesAndForests
using NamedGraphs
using NamedGraphs: hexagonal_lattice_graph, triangular_lattice_graph
gs = [
("Chain", named_grid((6, 1))),
("Cubic Lattice", named_grid((3, 3, 3))),
("Hexagonal Grid", hexagonal_lattice_graph(6, 6)),
("Comb Tree", named_comb_tree((4, 4))),
("Square lattice", named_grid((10, 10))),
("Triangular Grid", triangular_lattice_graph(5, 5; periodic=true)),
]
algs = [NamedGraphs.BFS(), NamedGraphs.DFS(), NamedGraphs.RandomBFS()]
end

@testset "Test Spanning Trees $g_string, $alg" for (g_string, g) in TestTreesAndForests.gs,
alg in TestTreesAndForests.algs

s_tree = spanning_tree(g; alg)
@test is_tree(s_tree)
@test Set(vertices(s_tree)) == Set(vertices(g))
@test issubset(Set(edges(s_tree)), Set(edges(g)))
end

@testset "Test Forest Cover $g_string" for (g_string, g) in TestTreesAndForests.gs
cover = forest_cover(g)
cover_edges = reduce(vcat, edges.(cover))
@test issetequal(cover_edges, edges(g))
@test all(issetequal(vertices(forest), vertices(g)) for forest in cover)
for forest in cover
trees = NamedGraph[forest[vs] for vs in connected_components(forest)]
@test all(is_tree.(trees))
end
end
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