diff --git a/report/report.tex b/report/report.tex
index 0ceebdc..0c90747 100644
--- a/report/report.tex
+++ b/report/report.tex
@@ -420,7 +420,13 @@ VF2 algorithm~\cite{cordella2004sub}, published in 2004. This algorithm is
 mostly Ullmann's algorithm, transcribed in a recursive writing, with the
 addition of five heuristics. \qtodo{Why not use it then?}
 
-\todo{Describe Ullmann}
+Ullmann is a widely used and fast algorithm for this problem. It makes an
+extensive use of adjacency matrix description of the graph, and the initial
+article takes advantage of the representation of those matrices as bitsets to
+make extensive use of bitwise operations.
+
+The to-be-built permutation matrix is a $\card{needle} \times \card{haystack}$
+matrix, 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Performance}
@@ -432,6 +438,8 @@ addition of five heuristics. \qtodo{Why not use it then?}
 There were a few observed cases where the algorithm tends to be slower on
 certain configurations.
 
+\todo{More corner cases}
+
 \paragraph{Split/merge trees.} A common pattern that tends to slow down the
 algorithm is split/merge trees. Those patterns occur when one wants to merge
 $n$ one bit wires into a single $n$ bits wire, or the other way around.
@@ -444,9 +452,16 @@ tree of depth \eg{} 8, a node just below the root will need a signature of
 order 7 to have a different signature than another one at the same depth. With
 a signature of order up to 6, only other gates from the tree will be included
 in the signature when going down in the tree; the exact same gates will be
-included above the tree's root. Thus, nothing will differentiate one gate from another while
-the boundary of the tree is not reached (assuming the gates below the tree's
-leaves are not all the same; if so, more levels will be needed).
+included above the tree's root. Thus, nothing will differentiate one gate from
+another while the boundary of the tree is not reached (assuming the gates below
+the tree's leaves are not all the same; if so, more levels will be needed).
+
+As the notion of ``left child'' and ``right child'' cannot be used (since it
+would rely on the order or description of the graph), there seems to be no good
+way to discriminate those two nodes. Furthermore, the nodes are not totally
+interchangeable: indeed, when checking for an equality between two such trees,
+it does not matter which node is the left one; but once this is fixed, the
+nodes on the layer below cannot be freely exchanged.
 
 \todo{Figure describing the problem}