The algorithm initializes a (m+1)-by-(n+1) matrix DP to store the optimal sentence alignment score.
dP[i+1,j+1] records the best score for aligning sentences between Sento,1,…, Sento,i and Sents,1,…, Sents,j (Step 2) where 1≤i≤m, the number of the sentences in Arto, and 1≤j≤n, the number of the sentences in Arts.