A new constrained edit distance between quotiented ordered trees

In this paper we propose a dynamic programming algorithm to compare two quotiented ordered trees using a constrained edit distance. An ordered tree is a tree in which the left-to-right order among siblings is significant. A quotiented ordered tree is an ordered tree T with an equivalence relation on vertices and such that, when the equivalence classes are collapsed to super-nodes, the graph so obtained is an ordered tree as well. Based on an algorithm proposed by Zhang and Shasha (1989, SIAM J. Comput., 18, 1245-1262) and introducing new notations, we describe a tree edit distance between quotiented ordered trees preserving equivalence relations on vertices during computation which works in polynomial time. Its application to RNA secondary structures comparison is finally presented.