Figure 2
Local tree structure for a given cell of D . Schematic representation of the content of a cell in the dynamic programming matrix. Suppose the cell is related to the association p:h and let p 1,p 2 be the two children of p. One single cell-root node is created to represent the association p:h (the circular node in the picture). This association has a local minimum cost c that can be obtained in different ways, that is choosing different associations for p1 and p2. Each equivalent alternative is represented by a node (squared in the picture). The number of alternatives is variable. In this example, we have three alternatives: (i) p 1 is mapped into h x and p 2 is mapped into h y ; (ii) p 1 is mapped into h and p 2 is mapped into h w ; and, (iii) p 1 and p 2 are both mapped into h z . Each one of these alternatives, combined with the mapping of p into h give the same local minimum cost c. Notice that, h, h w , h x , h y , and h z are distinct nodes of the host tree.