An Improved Algorithm for Tree Edit Distance Incorporating Structural Linearity

An ordered labeled tree is a tree in which the nodes are labeled and the left-to-right order among siblings is significant. The edit distance between two ordered labeled trees is the minimum cost of transforming one tree into the other by a sequence of edit operations. Among the best known tree edit distance algorithms, the majority can be categorized in terms of a framework named cover strategy. In this paper, we investigate how certain locally linear features may be utilized to improve the time complexity for computing the tree edit distance. We define structural linearity and present a method incorporating linearity which can work with existing cover-strategy based tree algorithms. We show that by this method the time complexity for an input of size n becomes O(n2 + φ(A, ñ)) where φ(A, ñ) is the time complexity of any cover-strategy algorithm A applied to an input size ñ, with ñ ≤ n, and the magnitude of ñ is reversely related to the degree of linearity. This result is an improvement of previous results when ñ < n and would be useful for situations in which ñ is in general substantially smaller than n, such as RNA secondary structure comparisons in computational biology.