Replace num_edges_per_tree by tree_edge_indices in TreeSet (#237)

* Replace num_edges_per_tree by tree_edge_indices in TreeSet

* Update two comments

---------

Co-authored-by: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>

Author: amontoison

src/coloring.jl

@@ -376,7 +376,8 @@ $TYPEDFIELDS
 struct TreeSet{T}
     reverse_bfs_orders::Vector{Tuple{T,T}}
     is_star::Vector{Bool}
-    num_edges_per_tree::Vector{T}
+    tree_edge_indices::Vector{T}
+    nt::T
 end
 
 function TreeSet(
@@ -388,20 +389,20 @@ function TreeSet(
     S = pattern(g)
     edge_to_index = edge_indices(g)
     nv = nb_vertices(g)
-    nt = forest.num_trees
+    (; nt, ranks) = forest
 
     # root_to_tree is a vector that maps a tree's root to the index of the tree
-    # We can recycle forest.ranks because we don't need it anymore to merge trees
-    root_to_tree = forest.ranks
+    # We can recycle the vector "ranks" because we don't need it anymore to merge trees
+    root_to_tree = ranks
     fill!(root_to_tree, zero(T))
 
-    # Contains the number of edges per tree
-    num_edges_per_tree = zeros(T, nt)
+    # vector specifying the starting and ending indices of edges for each tree
+    tree_edge_indices = zeros(T, nt + 1)
 
     # vector of dictionaries where each dictionary stores the neighbors of each vertex in a tree
     trees = [Dict{T,Vector{T}}() for i in 1:nt]
 
-    # current number of roots found
+    # number of roots found
     nr = 0
 
     rvS = rowvals(S)
@@ -418,18 +419,20 @@ function TreeSet(
                     root_to_tree[root] = nr
                 end
 
-                # index of the tree T that contains this edge
+                # index of the tree that contains this edge
                 index_tree = root_to_tree[root]
-                num_edges_per_tree[index_tree] += 1
 
-                # Update the neighbors of i in the tree T
+                # Update the number of edges for the current tree (shifted by 1 to facilitate the final cumsum)
+                tree_edge_indices[index_tree + 1] += 1
+
+                # Update the neighbors of i in the current tree
                 if !haskey(trees[index_tree], i)
                     trees[index_tree][i] = [j]
                 else
                     push!(trees[index_tree][i], j)
                 end
 
-                # Update the neighbors of j in the tree T
+                # Update the neighbors of j in the current tree
                 if !haskey(trees[index_tree], j)
                     trees[index_tree][j] = [i]
                 else
@@ -439,6 +442,12 @@ function TreeSet(
         end
     end
 
+    # Compute a shifted cumulative sum of tree_edge_indices, starting from one
+    tree_edge_indices[1] = one(T)
+    for k in 2:(nt + 1)
+        tree_edge_indices[k] += tree_edge_indices[k - 1]
+    end
+
     # degrees is a vector of integers that stores the degree of each vertex in a tree
     degrees = buffer
 
@@ -529,7 +538,7 @@ function TreeSet(
         is_star[k] = bool_star
     end
 
-    return TreeSet(reverse_bfs_orders, is_star, num_edges_per_tree)
+    return TreeSet(reverse_bfs_orders, is_star, tree_edge_indices, nt)
 end
 
 ## Postprocessing, mirrors decompression code
@@ -597,15 +606,17 @@ function postprocess!(
         end
     else
         # only the colors of non-leaf vertices are used
-        (; reverse_bfs_orders, is_star, num_edges_per_tree) = star_or_tree_set
+        (; reverse_bfs_orders, is_star, tree_edge_indices, nt) = star_or_tree_set
         nb_trivial_trees = 0
 
-        # Index of the first edge in reverse_bfs_orders for the current tree
-        first = 1
-
         # Iterate through all non-trivial trees
-        for k in eachindex(num_edges_per_tree)
-            ne_tree = num_edges_per_tree[k]
+        for k in 1:nt
+            # Position of the first edge in the tree
+            first = tree_edge_indices[k]
+
+            # Total number of edges in the tree
+            ne_tree = tree_edge_indices[k + 1] - first
+
             # Check if we have more than one edge in the tree (non-trivial tree)
             if ne_tree > 1
                 # Determine if the tree is a star
@@ -622,14 +633,17 @@ function postprocess!(
             else
                 nb_trivial_trees += 1
             end
-            first += ne_tree
         end
 
         # Process the trivial trees (if any)
         if nb_trivial_trees > 0
-            first = 1
-            for k in eachindex(num_edges_per_tree)
-                ne_tree = num_edges_per_tree[k]
+            for k in 1:nt
+                # Position of the first edge in the tree
+                first = tree_edge_indices[k]
+
+                # Total number of edges in the tree
+                ne_tree = tree_edge_indices[k + 1] - first
+
                 # Check if we have exactly one edge in the tree
                 if ne_tree == 1
                     (i, j) = reverse_bfs_orders[first]
@@ -642,7 +656,6 @@ function postprocess!(
                         color_used[color[j]] = true
                     end
                 end
-                first += ne_tree
             end
         end
     end

src/decompression.jl

@@ -517,7 +517,7 @@ end
 function decompress!(
     A::AbstractMatrix, B::AbstractMatrix, result::TreeSetColoringResult, uplo::Symbol=:F
 )
-    (; ag, color, reverse_bfs_orders, num_edges_per_tree, buffer) = result
+    (; ag, color, reverse_bfs_orders, tree_edge_indices, nt, buffer) = result
     (; S) = ag
     uplo == :F && check_same_pattern(A, S)
     R = eltype(A)
@@ -538,13 +538,11 @@ function decompress!(
         end
     end
 
-    # Index of the first edge in reverse_bfs_orders for the current tree
-    first = 1
-
     # Recover the off-diagonal coefficients of A
-    for k in eachindex(num_edges_per_tree)
-        ne_tree = num_edges_per_tree[k]
-        last = first + ne_tree - 1
+    for k in 1:nt
+        # Positions of the edges for each tree
+        first = tree_edge_indices[k]
+        last = tree_edge_indices[k + 1] - 1
 
         # Reset the buffer to zero for all vertices in a tree (except the root)
         for pos in first:last
@@ -567,7 +565,6 @@ function decompress!(
                 A[j, i] = val
             end
         end
-        first += ne_tree
     end
     return A
 end
@@ -582,7 +579,8 @@ function decompress!(
         ag,
         color,
         reverse_bfs_orders,
-        num_edges_per_tree,
+        tree_edge_indices,
+        nt,
         diagonal_indices,
         diagonal_nzind,
         lower_triangle_offsets,
@@ -622,16 +620,14 @@ function decompress!(
         end
     end
 
-    # Index of the first edge in reverse_bfs_orders for the current tree
-    first = 1
-
     # Index of offsets in lower_triangle_offsets and upper_triangle_offsets
     counter = 0
 
     # Recover the off-diagonal coefficients of A
-    for k in eachindex(num_edges_per_tree)
-        ne_tree = num_edges_per_tree[k]
-        last = first + ne_tree - 1
+    for k in 1:nt
+        # Positions of the edges for each tree
+        first = tree_edge_indices[k]
+        last = tree_edge_indices[k + 1] - 1
 
         # Reset the buffer to zero for all vertices in a tree (except the root)
         for pos in first:last
@@ -683,7 +679,6 @@ function decompress!(
             end
             #! format: on
         end
-        first += ne_tree
     end
     return A
 end

src/forest.jl

@@ -11,18 +11,18 @@ $TYPEDFIELDS
 """
 mutable struct Forest{T<:Integer}
     "current number of distinct trees in the forest"
-    num_trees::T
+    nt::T
     "vector storing the index of a parent in the tree for each edge, used in union-find operations"
     parents::Vector{T}
     "vector approximating the depth of each tree to optimize path compression"
     ranks::Vector{T}
 end
 
 function Forest{T}(n::Integer) where {T<:Integer}
-    num_trees = T(n)
+    nt = T(n)
     parents = collect(Base.OneTo(T(n)))
     ranks = zeros(T, T(n))
-    return Forest{T}(num_trees, parents, ranks)
+    return Forest{T}(nt, parents, ranks)
 end
 
 function _find_root!(parents::Vector{T}, index_edge::T) where {T<:Integer}
@@ -49,6 +49,6 @@ function root_union!(forest::Forest{T}, index_edge1::T, index_edge2::T) where {T
         rks[index_edge1] += one(T)
     end
     parents[index_edge2] = index_edge1
-    forest.num_trees -= one(T)
+    forest.nt -= one(T)
     return nothing
 end

src/result.jl

@@ -314,7 +314,8 @@ struct TreeSetColoringResult{
     color::Vector{T}
     group::GT
     reverse_bfs_orders::Vector{Tuple{T,T}}
-    num_edges_per_tree::Vector{T}
+    tree_edge_indices::Vector{T}
+    nt::T
     diagonal_indices::Vector{T}
     diagonal_nzind::Vector{T}
     lower_triangle_offsets::Vector{T}
@@ -329,7 +330,7 @@ function TreeSetColoringResult(
     tree_set::TreeSet{<:Integer},
     decompression_eltype::Type{R},
 ) where {T<:Integer,R}
-    (; reverse_bfs_orders, num_edges_per_tree) = tree_set
+    (; reverse_bfs_orders, tree_edge_indices, nt) = tree_set
     (; S) = ag
     nvertices = length(color)
     group = group_by_color(T, color)
@@ -358,15 +359,13 @@ function TreeSetColoringResult(
     lower_triangle_offsets = Vector{T}(undef, nedges)
     upper_triangle_offsets = Vector{T}(undef, nedges)
 
-    # Index of the first edge in reverse_bfs_orders for the current tree
-    first = 1
-
     # Index in lower_triangle_offsets and upper_triangle_offsets
     index_offsets = 0
 
-    for k in eachindex(num_edges_per_tree)
-        ne_tree = num_edges_per_tree[k]
-        last = first + ne_tree - 1
+    for k in 1:nt
+        # Positions of the edges for each tree
+        first = tree_edge_indices[k]
+        last = tree_edge_indices[k + 1] - 1
 
         for pos in first:last
             (leaf, neighbor) = reverse_bfs_orders[pos]
@@ -400,7 +399,6 @@ function TreeSetColoringResult(
             end
             #! format: on
         end
-        first += ne_tree
     end
 
     # buffer holds the sum of edge values for subtrees in a tree.
@@ -413,7 +411,8 @@ function TreeSetColoringResult(
         color,
         group,
         reverse_bfs_orders,
-        num_edges_per_tree,
+        tree_edge_indices,
+        nt,
         diagonal_indices,
         diagonal_nzind,
         lower_triangle_offsets,

test/forest.jl

@@ -3,7 +3,7 @@ using Test
 
 @testset "Constructor Forest" begin
     forest = Forest{Int}(5)
-    @test forest.num_trees == 5
+    @test forest.nt == 5
     @test length(forest.parents) == 5
     @test all(forest.parents .== 1:5)
     @test all(forest.ranks .== 0)
@@ -27,7 +27,7 @@ end
     @test forest.parents[3] == 1
     @test forest.ranks[1] == 1
     @test forest.ranks[3] == 0
-    @test forest.num_trees == 4
+    @test forest.nt == 4
 
     root1 = find_root!(forest, 1)
     root2 = find_root!(forest, 2)
@@ -39,5 +39,5 @@ end
     @test forest.parents[2] == 1
     @test forest.ranks[1] == 1
     @test forest.ranks[2] == 0
-    @test forest.num_trees == 3
+    @test forest.nt == 3
 end