Computing the Edit-Distance Between Unrooted Ordered Trees

Abstract

Abstract. An ordered tree is a tree in which each node's incident edges are cyclically ordered; think of the tree as being embedded in the plane. Let A and B be two ordered trees. The edit distance between A and B is the minimum cost of a sequence of operations (contract an edge, uncontract an edge, modify the label of an edge) needed to transform A into B. We give an O(n 3 log n) algorithm to compute the edit distance between two ordered trees.

Normalized Similarity of RNA Sequences

“…1). In [15], an algorithm for tree editing was presented which was later improved in [13]. This algorithm can be used to determine the minimum number of unpaired base and arc deletions needed in order to obtain a common subsequence of R 1 and R 2 in O(n 2 m lg m) time, and is currently the fastest (worst-case) algorithm for computing the global LCS score of two RNA sequences [4].…”

“…In the second phase, the algorithm computes and stores the longest common subsequence of R 1 [i, i ′ ] and R 2 [j, j ′ ] for every (i, i ′ ) ∈ P 1 and (j, j ′ ) ∈ P 2 . As mentioned in Section 2.2, this can be done by a single execution of the algorithm given in [13].…”

“…Using [13] allows us to compute this efficiently, in some cases at the cost of computing M for a single pair. On the other hand, in cases where the number of nesting edges is small, one can use standard LCS algorithms.…”

“…The preprocessing stage can be done in O(n 2 m lg m) time using the algorithm in [13]. Furthermore, computing all DP requires O(n 2 m) time.…”

“…We present an O(n 2 m lg m) time algorithm for this problem which is conceptually inspired by the algorithm given in [7]. Its time complexity origins in the global LCS algorithm presented in [13], which is used as a preprocessing procedure in the algorithm. Therefore, our algorithm can compute the local normalized LCS score at the cost of computing the global LCS score.…”