We present a systematic treatment of alignment distance and local similarity algorithms on trees and forests. We build upon the tree alignment algorithm for ordered trees given by Jiang et. al (1995) and extend it to calculate local forest alignments, which is essential for finding local similar regions in RNA secondary structures. The time complexity of our algorithm is  Motivation RNA is a chain molecule, mathematically a string over a four letter alphabet. It is built from nucleotides containing the bases A(denine), C(ytosine), G(uanine), and U(racil). By folding back onto itself, an RNA molecule forms structure, stabilized by the forces of hydrogen bonds between certain pairs of bases (A-U, C-G, G-U), and dense stacking of neighbouring base pairs. The investigation of RNA secondary structures is a challenging task in molecular biology. RNA molecules have a large variety of functions in the cell which often depend on special structural properties. String edit distance [25] clearly is the most successful model in sequence comparison. It is used in document processing, file comparison, molecular sequence analysis, and numerous other applications of approximate string matching. The basic model is that one string is "edited" into another string by a sequence of edit operations, such as single character replacement (R), deletion (D) or insertion (I). The weights associated with the edit operations sum up to an overall score, and the edit sequence giving the minimal score defines the edit distance of the two strings. Equivalently, the editing process, ignoring the order of edit operations, can be represented as an alignment. This equivalence does not generalize to trees, as already mentioned in [1] . For each tree alignment one can construct a corresponding sequence of edit operations, but not vice versa. One can understand editing as finding a largest common sub-structure, while aligning means finding the smallest common superstructure (In fact, this depends on the scoring scheme.). Which model is favourable depends on the problem. The first generalization of the edit model from strings to rooted ordered trees is due to [23] , algorithmically improved in [31] and implemented and applied to computa-
H€ ochsmann et al. REF developed another approach for detecting local similarities in RNA secondary structures.
Local similarity in RNA secondary structures
Computational Systems Bioinformatics. CSB2003. Proceedings of the 2003 IEEE Bioinformatics Conference. CSB2003
Computational Systems Bioinformatics. CSB2003. Proceedings of the 2003 IEEE Bioinformatics Conference. CSB2003
Computer Science Medicine