(A) Sparsification of secondary structure folding. Suppose the optimal solution Li,j is obtained from the optimal solutions Li,k, Lk + 1,q and Lq + 1,j. Based on the recursions of the secondary structures, Li,kand Lk + 1,q produce an optimal solution of Li,q. Similarly, Lk + 1,q and Lq + 1,j produce an optimal solution of Lk + 1,j. Now, in order to obtain an optimal solution of Li,j it is sufficient to consider either the grouping Li,q and Lq + 1,j or Li,k and Lk + 1,j. (B) General idea of sparsification: L
is alternatively realized via and, or and. Thus it is sufficient to only consider one of the computation paths.