A Clique-Based Method Using Dynamic Programming for Computing Edit Distance Between Unordered Trees

Abstract

Many kinds of tree-structured data, such as RNA secondary structures, have become available due to the progress of techniques in the field of molecular biology. To analyze the treestructured data, various measures for computing the similarity between them have been developed and applied. Among them, tree edit distance is one of the most widely used measures. However, the tree edit distance problem for unordered trees is NP-hard. Therefore, it is required to develop efficient algorithms for the problem. Recently, a practical method called clique-based algorithm has been proposed, but it is not fast for large trees.This article presents an improved clique-based method for the tree edit distance problem for unordered trees. The improved method is obtained by introducing a dynamic programming scheme and heuristic techniques to the previous clique-based method. To evaluate the efficiency of the improved method, we applied the method to comparison of real tree structured data such as glycan structures. For large tree-structures, the improved method is much faster than the previous method. In particular, for hard instances, the improved method achieved more than 100 times speed-up.

A Simple and Faster Branch-and-Bound Algorithm for Finding a Maximum Clique with Computational Experiments

“…MCS is also successfully applied to solve a problem in bioinformatics [24] where preliminary experiments confirmed the superiority of MCS over MCR and MCQ for this problem.…”

“…Nevertheless, we have many practical problems that can be formulated as maximum clique problems. Such examples abound in bioinformatics [1]- [4], [8], [24], [49], drug design [8], pattern recognition and image processing [27], [2], [16], clustering [52], data mining [23], design of quantum circuits [26], design of DNA and RNA sequences for biomolecular computation [19], coding theory [35], design of wireless networks [22], and many others [6].…”

Anchored Alignment Distance between Rooted Labeled Unordered Trees

“…Concerned with Section IV-B, Mori et al [9] and Yoshino et al [14] have designed the algorithms to compute unordered tree edit distance τ TAI exactly for a part of N-glycan data. Section IV-B claims that the number of pairs that τ ALN < τ ACH and τ ALN < τ ACH is much smaller than the number of pairs that τ ALN = τ ACH and τ ALN = τ ILST .…”

A Much Faster Algorithm for Finding a Maximum Clique with Computational Experiments

“…Here, finding a maximum clique in a graph has many important practical applications. These applications include coding theory [24], pattern recognition and image processing [9], [20], bioinformatics [5], [18], [33], design of wireless networks [16], and others [4], [36], [37].…”