A remark on the subsequence problem for arc-annotated sequences with pairwise nested arcs

The Arc-Preserving Subsequence (APS) problem appears in the comparison of RNA structures in computational biology. Given two arc-annotated sequences of length n and m, APS asks if the shorter sequence (length m) can be obtained from the longer one by deleting certain elements along with their incident arcs. It is known that APS with pairwise nested arcs can be solved in O(mn) time. We give an algorithm running in O(m*m+n) time in the worst case, actually it is even faster in particular if the shorter sequence has many arcs. The result may serve as a buidling block for improved APS algorithms in the general case