Fast RNA structure alignment for crossing input structures

The complexity of pairwise RNA structure alignment depends on the structural restrictions assumed for both the input structures and the computed consensus structure. For arbitrarily crossing input and consensus structures, the problem is NP-hard. For non-crossing consensus structures, Jiang et al.'s (2002) [9] algorithm computes the alignment in O(n2m2) time where n and m denote the lengths of the two input sequences. If the input structures are also non-crossing, the problem corresponds to tree editing which can be solved in O(m2n(1+lognm)) time (Demaine et al., 2007) [3]. We present a new algorithm that solves the problem for d-crossing structures in O(dm2nlogn) time, where d is a parameter that is one for non-crossing structures, bounded by n for crossing structures, and much smaller than n on many practical examples. Crossing input structures allow for applications where the input is not a fixed structure but is given as base-pair probability matrices.