Efficient chaining of seeds in ordered trees

We consider the problem of chaining seeds in ordered trees. Seeds are mappings between two trees Q and T and a chain is a subset of non-overlapping seeds that is consistent with respect to postfix order and ancestrality. This problem is a natural extension of a similar problem for sequences, and has applications in computational biology, such as mining a database of RNA secondary structures. For the chaining problem with a set S of m   seeds of cumulated size ‖S‖‖S‖, we describe an algorithm with complexity O(‖S‖log(‖S‖)+m‖S‖log(m))O(‖S‖log(‖S‖)+m‖S‖log(m)) in time and O(m‖S‖)O(m‖S‖) in space.