diff --git a/src/decompression.jl b/src/decompression.jl
index 6b127fa..005fe8f 100644
--- a/src/decompression.jl
+++ b/src/decompression.jl
@@ -372,18 +372,18 @@ function decompress_acyclic!(
 
     # to be optimized!
     set_roots = Set{Int}()
-    roots = Int[]
     ntrees = 0
     for edge in tree_set.disjoint_sets.revmap
+        # ensure that all paths are compressed
         root_edge = find_root!(disjoint_sets, edge)
         root_index = tree_set.disjoint_sets.intmap[root_edge]
-        push!(roots, root_index)
 
         # we exclude trees related to diagonal coefficients
         if (edge[1] != edge[2])
             push!(set_roots, root_index)
         end
     end
+    roots = disjoint_sets.internal.parents
 
     # DEBUG
     println(set_roots)
@@ -400,16 +400,14 @@ function decompress_acyclic!(
             end
         end
     end
-    for k in 1:ntrees
-        nedges = length(trees[k])
-        if nedges > 1
-            tree_edges = trees[k]
-            tree_ranks = view(disjoint_sets.internal.ranks, tree_edges)
-            p = sortperm(tree_ranks)
-            trees[k] = tree_edges[p]
-            display(disjoint_sets.internal.ranks[trees[k]])
-        end
-    end
+    # for k in 1:ntrees
+    #     nedges = length(trees[k])
+    #     if nedges > 1
+    #         tree_edges = trees[k]
+    #         p = ...
+    #         trees[k] = tree_edges[p]
+    #     end
+    # end
 
     # DEBUG
     display(trees)
@@ -439,7 +437,7 @@ function decompress_acyclic!(
                 stored_values[i] = zero(R)
                 stored_values[j] = zero(R)
             end
-            for edge_index in tree  # edges are sorted by their rank using disjoint_sets.internal.rank
+            for edge_index in tree  # edges are sorted by their distance to the root
                 i, j = disjoint_sets.revmap[edge_index]
                 parent_index = disjoint_sets.internal.parents[edge_index]
                 k, l = disjoint_sets.revmap[parent_index]