  An ordered labeled tree is a tree in which the nodes are labeled and the
left-to-right order among siblings is relevant. The edit distance between two
ordered labeled trees is the minimum cost of changing one tree into the other
through a sequence of edit steps. In the literature, there are a class of
algorithms based on different yet closely related path-decomposition schemes.
This article reviews the principles of these algorithms, and studies the
concepts related to the algorithmic complexities as a consequence of the
decomposition schemes.
