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Move all subroutines in star_coloring and acyclic_coloring #239

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Move all subroutines in star_coloring and acyclic_coloring #239

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195 changes: 60 additions & 135 deletions src/coloring.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -99,10 +99,20 @@ function star_coloring(
if p == v # Case 1
if treated[q] != v
# forbid colors of neighbors of q
_treat!(treated, forbidden_colors, g, v, q, color)
for x in neighbors(g, q)
!has_diagonal(g) || (q == x && continue)
iszero(color[x]) && continue
forbidden_colors[color[x]] = v
end
treated[q] = v
end
# forbid colors of neighbors of w
_treat!(treated, forbidden_colors, g, v, w, color)
for x in neighbors(g, w)
!has_diagonal(g) || (w == x && continue)
iszero(color[x]) && continue
forbidden_colors[color[x]] = v
end
treated[w] = v
else
first_neighbor[color[w]] = (v, w, index_vw)
for (x, index_wx) in neighbors_with_edge_indices(g, w)
Expand All @@ -120,7 +130,32 @@ function star_coloring(
break
end
end
_update_stars!(star, hub, g, v, color, first_neighbor)
for (w, index_vw) in neighbors_with_edge_indices(g, v)
!has_diagonal(g) || (v == w && continue)
iszero(color[w]) && continue
x_exists = false
for (x, index_wx) in neighbors_with_edge_indices(g, w)
!has_diagonal(g) || (w == x && continue)
if x != v && color[x] == color[v] # vw, wx ∈ E
star_wx = star[index_wx]
hub[star_wx] = w # this may already be true
star[index_vw] = star_wx
x_exists = true
break
end
end
if !x_exists
(p, q, index_pq) = first_neighbor[color[w]]
if p == v && q != w # vw, vq ∈ E and color[w] = color[q]
star_vq = star[index_pq]
hub[star_vq] = v # this may already be true
star[index_vw] = star_vq
else # vw forms a new star
push!(hub, -max(v, w)) # star is trivial (composed only of two vertices) so we set the hub to a negative value, but it allows us to choose one of the two vertices
star[index_vw] = length(hub)
end
end
end
end
star_set = StarSet(star, hub)
if postprocessing
Expand All @@ -131,64 +166,6 @@ function star_coloring(
return color, star_set
end

function _treat!(
# modified
treated::AbstractVector{<:Integer},
forbidden_colors::AbstractVector{<:Integer},
# not modified
g::AdjacencyGraph,
v::Integer,
w::Integer,
color::AbstractVector{<:Integer},
)
for x in neighbors(g, w)
!has_diagonal(g) || (w == x && continue)
iszero(color[x]) && continue
forbidden_colors[color[x]] = v
end
treated[w] = v
return nothing
end

function _update_stars!(
# modified
star::AbstractVector{<:Integer},
hub::AbstractVector{<:Integer},
# not modified
g::AdjacencyGraph,
v::Integer,
color::AbstractVector{<:Integer},
first_neighbor::AbstractVector{<:Tuple},
)
for (w, index_vw) in neighbors_with_edge_indices(g, v)
!has_diagonal(g) || (v == w && continue)
iszero(color[w]) && continue
x_exists = false
for (x, index_wx) in neighbors_with_edge_indices(g, w)
!has_diagonal(g) || (w == x && continue)
if x != v && color[x] == color[v] # vw, wx ∈ E
star_wx = star[index_wx]
hub[star_wx] = w # this may already be true
star[index_vw] = star_wx
x_exists = true
break
end
end
if !x_exists
(p, q, index_pq) = first_neighbor[color[w]]
if p == v && q != w # vw, vq ∈ E and color[w] = color[q]
star_vq = star[index_pq]
hub[star_vq] = v # this may already be true
star[index_vw] = star_vq
else # vw forms a new star
push!(hub, -max(v, w)) # star is trivial (composed only of two vertices) so we set the hub to a negative value, but it allows us to choose one of the two vertices
star[index_vw] = length(hub)
end
end
end
return nothing
end

"""
StarSet

Expand Down Expand Up @@ -254,16 +231,13 @@ function acyclic_coloring(
!has_diagonal(g) || (w == x && continue)
iszero(color[x]) && continue
if forbidden_colors[color[x]] != v
_prevent_cycle!(
v,
w,
x,
index_wx,
color,
first_visit_to_tree,
forbidden_colors,
forest,
)
root_wx = find_root!(forest, index_wx) # root of the 2-colored tree to which the edge wx belongs
(p, q) = first_visit_to_tree[root_wx]
if p != v # T is being visited from vertex v for the first time
first_visit_to_tree[root_wx] = (v, w)
elseif q != w # T is connected to vertex v via at least two edges
forbidden_colors[color[x]] = v
end
end
end
end
Expand All @@ -276,7 +250,15 @@ function acyclic_coloring(
for (w, index_vw) in neighbors_with_edge_indices(g, v) # grow two-colored stars around the vertex v
!has_diagonal(g) || (v == w && continue)
iszero(color[w]) && continue
_grow_star!(v, w, index_vw, color, first_neighbor, forest)
# Create a new tree T_{vw} consisting only of edge vw
(p, q, index_pq) = first_neighbor[color[w]]
if p != v # a neighbor of v with color[w] encountered for the first time
first_neighbor[color[w]] = (v, w, index_vw)
else # merge T_{vw} with a two-colored star being grown around v
root_vw = find_root!(forest, index_vw)
root_pq = find_root!(forest, index_pq)
root_union!(forest, root_vw, root_pq)
end
end
for (w, index_vw) in neighbors_with_edge_indices(g, v)
!has_diagonal(g) || (v == w && continue)
Expand All @@ -285,7 +267,12 @@ function acyclic_coloring(
!has_diagonal(g) || (w == x && continue)
(x == v || iszero(color[x])) && continue
if color[x] == color[v]
_merge_trees!(v, w, x, index_vw, index_wx, forest) # merge trees T₁ ∋ vw and T₂ ∋ wx if T₁ != T₂
# merge trees T₁ ∋ vw and T₂ ∋ wx if T₁ != T₂
root_vw = find_root!(forest, index_vw)
root_wx = find_root!(forest, index_wx)
if root_vw != root_wx
root_union!(forest, root_vw, root_wx)
end
end
end
end
Expand All @@ -302,68 +289,6 @@ function acyclic_coloring(
return color, tree_set
end

function _prevent_cycle!(
# not modified
v::Integer,
w::Integer,
x::Integer,
index_wx::Integer,
color::AbstractVector{<:Integer},
# modified
first_visit_to_tree::AbstractVector{<:Tuple},
forbidden_colors::AbstractVector{<:Integer},
forest::Forest{<:Integer},
)
root_wx = find_root!(forest, index_wx) # The edge wx belongs to the 2-colored tree T, represented by an edge with an integer ID
(p, q) = first_visit_to_tree[root_wx]
if p != v # T is being visited from vertex v for the first time
first_visit_to_tree[root_wx] = (v, w)
elseif q != w # T is connected to vertex v via at least two edges
forbidden_colors[color[x]] = v
end
return nothing
end

function _grow_star!(
# not modified
v::Integer,
w::Integer,
index_vw::Integer,
color::AbstractVector{<:Integer},
# modified
first_neighbor::AbstractVector{<:Tuple},
forest::Forest{<:Integer},
)
# Create a new tree T_{vw} consisting only of edge vw
(p, q, index_pq) = first_neighbor[color[w]]
if p != v # a neighbor of v with color[w] encountered for the first time
first_neighbor[color[w]] = (v, w, index_vw)
else # merge T_{vw} with a two-colored star being grown around v
root_vw = find_root!(forest, index_vw)
root_pq = find_root!(forest, index_pq)
root_union!(forest, root_vw, root_pq)
end
return nothing
end

function _merge_trees!(
# not modified
v::Integer,
w::Integer,
x::Integer,
index_vw::Integer,
index_wx::Integer,
# modified
forest::Forest{<:Integer},
)
root_vw = find_root!(forest, index_vw)
root_wx = find_root!(forest, index_wx)
if root_vw != root_wx
root_union!(forest, root_vw, root_wx)
end
return nothing
end

"""
TreeSet

Expand Down