Tree Edit Distance Problem Research Articles

Tree Edit Distance and Maximum Agreement Subtree

This paper presents an interesting relation between the Maximum Agreement Subtree (MAST) problem and the Tree Edit Distance (TED) problem, both of which have been intensively studied in the literature. To be specific, we show that, for an arbitrary tree edit distance metric that is a derivative of the Taï tree edit distance metric, there exists a MAST-like pattern extraction problem, named Mostly Adjusted Sub-Forest (MASF) problem, such that computing a distance between trees x and y is equivalent to finding an optimal pattern shared between x and y. The MASF problem is different from the MAST problem in: (1) A pattern of the MASF problem may be a forest instead of a tree; (2) Instead of requiring exact match of labels, a pattern of a MASF problem is multi-labeled, and our flexible matching rule only requires that the label set of a vertex of a pattern includes the label of the corresponding vertex in a target tree; (3) To control ambiguity of matching caused by the flexible rule, the objective function includes a penalty function. As an application of this generic framework, we equate the Lu* tree edit distance metric with a pattern extraction problem, named the Mostly Adjusted Agreement Sub-Tree (MAAST) problem. The MAAST problem aims to find optimal agreement subtrees under the flexible matching rule and is solved in O(n2dlog⁡d)-time, where n and d are the size and the minimum degree of the input trees. The MAST problem requires O(n2.5)-time computation.

Content Evocation Using Web Scraping and Semantic Illustration

Web scraping is the process of automatically collecting information from the World Wide Web. It is a field with active developments, sharing a common goal with the semantic web vision, an ambitious initiative that still requires breakthroughs in text processing, artificial intelligence and human-computer interactions. It means extraction of content from different web pages using web scrapping and semantic illustration. Web Scrapping is a process of evocation of content from HTML pages and related to web indexing. A commonly used measure for tree similarity is the tree edit distance which easily can be extended to be a measure of how well a pattern can be matched in a tree. An obstacle for this approach is its time complexity, so we consider if faster algorithms for constrained tree edit distances are usable for web scraping, and to reduce the size of the tree representing the web page. Different applications of web scraping are used by current market to achieve best web scraping output, Like Web Data Extraction, Data Collection, Screen Scraping. Many different algorithms are used for web scraping like “tree pattern matching”, “tree mapping”, “approximate tree matching”. But in general “tree edit distance” algorithm is used. But with this algorithm many issues of incorrectness of data, low efficiency and higher time complexity have analyzed. In this research I am focus to improve the performance of tree edit distance problem. And I am also trying to focus on higher bound time complexity of this algorithm.

Covering tree with stars

We study the tree edit distance (TED) problem with edge deletions and edge insertions as edit operations. We reformulate a special case of this problem as Covering Tree with Stars (CTS): given a tree T and a set $$\mathcal {S}$$ S of stars, can we connect the stars in $$\mathcal {S}$$ S by adding edges between them such that the resulting tree is isomorphic to T? We prove that in the general setting, CST is NP-complete, which implies that the TED considered here is also NP-hard, even when both input trees have diameters bounded by 10. We also show that, when the number of distinct stars is bounded by a constant k, CTS can be solved in polynomial time, by presenting a dynamic programming algorithm running in $$O(|V(T)|^2\cdot k\cdot |V(\mathcal{S})|^{2k})$$ O ( | V ( T ) | 2 · k · | V ( S ) | 2 k ) time.

Approximation and parameterized algorithms for common subtrees and edit distance between unordered trees

Given two rooted, labeled, unordered trees, the common subtree problem is to find a bijective matching between subsets of nodes of the trees of maximum cardinality which preserves labels and ancestry relationship. The tree edit distance problem is to determine the least cost sequence of insertions, deletions and substitutions that converts a tree into another given tree. Both problems are known to be hard to approximate within some constant factor in general.We tackle these problems from two perspectives: giving exact algorithms, either for special cases or in terms of some parameters; and approximation algorithms and hardness of approximation. We present a parameterized algorithm in terms of the number of branching nodes that solves both problems and yields polynomial algorithms for several special classes of trees. This is complemented with a tighter APX-hardness proof that holds when the trees are of height one and two, respectively. Furthermore, we present the first approximation algorithms for both problems. In particular, for the common subtree problem for t trees, we present an algorithm achieving a tlog2(bOPT+1) ratio, where bOPT is the number of branching nodes in the optimal solution. We also present constant factor approximation algorithms for both problems in the case of bounded height trees.

A clique-based method using dynamic programming for computing edit distance between unordered trees.

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 tree-structured 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.

Exact algorithms for computing the tree edit distance between unordered trees

This paper presents a fixed-parameter algorithm for the tree edit distance problem for unordered trees under the unit cost model that works in O ( 2.6 2 k ⋅ p o l y ( n ) ) time and O ( n 2 ) space, where the parameter k is the maximum bound of the edit distance and n is the maximum size of input trees. This paper also presents polynomial-time algorithms for the case where the maximum degree of the largest common subtree is bounded by a constant.

Tree Edit Distance Problems: Algorithms and Applications to Bioinformatics

Tree structured data often appear in bioinformatics. For example, glycans, RNA secondary structures and phylogenetic trees usually have tree structures. Comparison of trees is one of fundamental tasks in analysis of these data. Various distance measures have been proposed and utilized for comparison of trees, among which extensive studies have been done on tree edit distance. In this paper, we review key results and our recent results on the tree edit distance problem and related problems. In particular, we review polynomial time exact algorithms and more efficient approximation algorithms for the edit distance problem for ordered trees, and approximation algorithms for the largest common sub-tree problem for unordered trees. We also review applications of tree edit distance and its variants to bioinformatics with focusing on comparison of glycan structures.

Faster algorithms for guided tree edit distance

The guided tree edit distance problem is to find a minimum cost series of edit operations that transforms two input forests F and G into isomorphic forests F ′ and G ′ such that a third input forest H is included in F ′ (and G ′ ). The edit operations are relabeling a vertex and deleting a vertex. We show efficient algorithms for this problem that are faster than the previous algorithm for this problem of Peng and Ting [Z. Peng, H. Ting, Guided forest edit distance: Better structure comparisons by using domain-knowledge, in: Proc. 18th Symposium on Combinatorial Pattern Matching (CPM), 2007, pp. 28–39].

Discovering Shape Classes using Tree Edit-Distance and Pairwise Clustering

This paper describes work aimed at the unsupervised learning of shape-classes from shock trees. We commence by considering how to compute the edit distance between weighted trees. We show how to transform the tree edit distance problem into a series of maximum weight clique problems, and show how to use relaxation labeling to find an approximate solution. This allows us to compute a set of pairwise distances between graph-structures. We show how the edit distances can be used to compute a matrix of pairwise affinities using ?2 statistics. We present a maximum likelihood method for clustering the graphs by iteratively updating the elements of the affinity matrix. This involves interleaved steps for updating the affinity matrix using an eigendecomposition method and updating the cluster membership indicators. We illustrate the new tree clustering framework on shock-graphs extracted from the silhouettes of 2D shapes.

A survey on tree edit distance and related problems

We survey the problem of comparing labeled trees based on simple local operations of deleting, inserting, and relabeling nodes. These operations lead to the tree edit distance, alignment distance, and inclusion problem. For each problem we review the results available and present, in detail, one or more of the central algorithms for solving the problem.

Decomposition algorithms for the tree edit distance problem

We study the behavior of dynamic programming methods for the tree edit distance problem, such as [P. Klein, Computing the edit-distance between unrooted ordered trees, in: Proceedings of 6th European Symposium on Algorithms, 1998, p. 91–102; K. Zhang, D. Shasha, SIAM J. Comput. 18 (6) (1989) 1245–1262]. We show that those two algorithms may be described as decomposition strategies. We introduce the general framework of cover strategies, and we provide an exact characterization of the complexity of cover strategies. This analysis allows us to define a new tree edit distance algorithm, that is optimal for cover strategies.

Computing approximate tree edit distance using relaxation labeling

This paper presents a new method for computing the tree edit distance problem with uniform edit cost. We commence by showing that any tree obtained with a sequence of cut operations is a subtree of the transitive closure of the original tree, we show that the necessary condition for any subtree to be a solution can be reduced to a clique problem in a derived structure. Using this idea we transform the problem of computing tree edit distance into a series of maximum weight clique problems. We, then use relaxation labeling to find an approximation to the tree edit distance.

A simplified graphical method for deriving system steady-state probability

This paper presents an interesting relation between the Maximum Agreement Subtree (MAST) problem and the Tree Edit Distance (TED) problem, both of which have been intensively studied in the literature. To be specific, we show that, for an arbitrary tree edit distance metric that is a derivative of the Taï tree edit distance metric, there exists a MAST-like pattern extraction problem, named Mostly Adjusted Sub-Forest (MASF) problem, such that computing a distance between trees x and y is equivalent to finding an optimal pattern shared between x and y. The MASF problem is different from the MAST problem in: (1) A pattern of the MASF problem may be a forest instead of a tree; (2) Instead of requiring exact match of labels, a pattern of a MASF problem is multi-labeled, and our flexible matching rule only requires that the label set of a vertex of a pattern includes the label of the corresponding vertex in a target tree; (3) To control ambiguity of matching caused by the flexible rule, the objective function includes a penalty function. As an application of this generic framework, we equate the Lu* tree edit distance metric with a pattern extraction problem, named the Mostly Adjusted Agreement Sub-Tree (MAAST) problem. The MAAST problem aims to find optimal agreement subtrees under the flexible matching rule and is solved in O(n2dlog⁡d)-time, where n and d are the size and the minimum degree of the input trees. The MAST problem requires O(n2.5)-time computation.