Simple Fast Algorithms for the Editing Distance between Trees and Related Problems

Abstract

Abstract. Ordered labeled trees are trees in which the left-to-right order among siblings is. significant. The distance between two ordered trees is considered to be the weighted number of edit operations (insert, delete, and modify) to transform one tree to another. The problem of approximate tree matching is also considered. Specifically, algorithms are designed to answer the following kinds of questions:1. What is the distance between two trees?2. What is the minimum distance between T and T when zero or more subtrees can be removed from T23. Let the pruning of a tree at node n mean removing all the descendants of node n. The analogous question for prunings as for subtrees is answered.A dynamic programming algorithm is presented to solve the three questions in sequential time O(I Tll x IT2lxmin (depth( Tt), leaves( T)) x min (depth(T2), leaves(T2))) and space O(Ir, x lT21) compared with o(I T,I IT=I x(depth(T)): x (depth(T2))) for the best previous published algorithm due to Tai [J. Assoc.Comput. Mach., 26 (1979)

Computing the Edit-Distance Between Unrooted Ordered Trees

“…The proof consists in combining a slight modification of Lemma 7 of Zhang and Shasha [10] with our Lemma 2.…”

A novel XML document structure comparison framework based-on sub-tree commonalities and label semantics

“…The resulting algorithm has a complexity of O(|A||B|× depth(A) 2 × depth(B) 2 ) when finding the edit distance between two trees A and B (|A| and |B| denote tree cardinalities while depth(A) and depth(B) are the depths of the trees). Similarly, early approaches in [70,89] allow insertion, deletion and relabeling of nodes anywhere in the tree. Yet, they remain greedy in complexity.…”

KF-Diff+: Highly Efficient Change Detection Algorithm for XML Documents

“…Since XML documents can be represented as trees, it is a natural idea to utilize tree-to-tree correction techniques to detect changes in XML documents. Zhang and Shasha proposed a fast algorithm to find the minimum cost editing distance between two ordered labeled trees [9]. Given two or-dered trees T 1 and T 2 , in which each node has an associated label, their algorithm finds an optimal edit script in time O(|T 1 | × |T 2 | × min {depth(T 1 ), leaves(T 1 )} × min {depth(T 2 ), leaves(T 2 ) }), which is the best known result for the general tree-to-tree correction problem.…”

“…MH-Diff [5] provides an efficient heuristic solution based on transforming the problem to the edge cover problem, with a worst case cost in O(n 2 logn), where n is the total number of nodes. XMLTreeDiff [3] use DOMHash [7] and Zhang's algorithm [9]. Since the former conflicts with the later, this method may not generate an optimal result.…”