Figure 1

Tree representation of the solution traces of the permutation  π  =(−3,2,1,−4). In this representation, only the values inside of solid boxes are reversals that effectively are in the structure. The values inside of dashed boxes are reversals which are optimal 1-sequences but, when combined with their parent trace, lead to traces that were inserted in another branch of the tree. The wide edges show the two traces which sort the permutation: {1}{1,2,3}{2}{4} and {1,2,4}{3}|{1,3,4}|{2,3,4}.