A faster and more space-efficient algorithm for inferring arc-annotations of RNA sequences through alignment

The nested arc-annotation of a sequence is an important model used to represent structural information for RNA and protein sequences. Given two sequences S1 and S2 and a nested arc-annotation P 1 for S1, this paper considers the problem of inferring the nested arc-annotation P2 for S2 such that (S 1, P1) and (S2, P2) have the largest common substructure. The problem has a direct application in predicting the secondary structure of an RNA sequence given a closely related sequence with known secondary structure. The currently most efficient algorithm for this problem requires O(nm3) time and O(nm2) space where n is the length of the sequence with known arc-annotation and m is the length of the sequence whose arc-annotation is to be inferred. By using sparsification on a new recursive dynamic programming algorithm and applying a Hirschberg-like traceback technique with compression, we obtain an improved algorithm that runs in min{O(nm2 + n2m),O(nm2 log n), O(nm 3) time and min{O(m2 + mn), O(m2 log n + n)} space.