A constrained edit distance algorithm between semi-ordered trees

AbstractIn this paper, we propose a formal definition of a new class of trees called semi-ordered trees and a polynomial dynamic programming algorithm to compute a constrained edit distance between such trees. The core of the method relies on a similar approach to compare unordered [Kaizhong Zhang, A constrained edit distance between unordered labeled trees, Algorithmica 15 (1996) 205–222] and ordered trees [Kaizhong Zhang, Algorithms for the constrained editing distance between ordered labeled trees and related problems, Pattern Recognition 28 (3) (1995) 463–474]. The method is currently applied to evaluate the similarity between architectures of apple trees [Vincent Segura, Aida Ouangraoua, Pascal Ferraro, Evelyne Costes, Comparison of tree architecture using tree edit distances: Application to two-year-old apple tree, Euphytica 161 (2007) 155–164]

A clique-based method for the edit distance between unordered trees and its application to analysis of glycan structures

[Background]Measuring similarities between tree structured data is important for analysis of RNA secondary structures, phylogenetic trees, glycan structures, and vascular trees. The edit distance is one of the most widely used measures for comparison of tree structured data. However, it is known that computation of the edit distance for rooted unordered trees is NP-hard. Furthermore, there is almost no available software tool that can compute the exact edit distance for unordered trees. [Results]In this paper, we present a practical method for computing the edit distance between rooted unordered trees. In this method, the edit distance problem for unordered trees is transformed into the maximum clique problem and then efficient solvers for the maximum clique problem are applied. We applied the proposed method to similar structure search for glycan structures. The result suggests that our proposed method can efficiently compute the edit distance for moderate size unordered trees. It also suggests that the proposed method has the accuracy comparative to those by the edit distance for ordered trees and by an existing method for glycan search. [Conclusions]The proposed method is simple but useful for computation of the edit distance between unordered trees. The object code is available upon request

On the Complexity of Tree Edit Distance with Variables

In this paper, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas. We analyze the computational complexity of several variants of this model. In particular, we show that the problem is NP-complete for ordered trees. We also show for unordered trees that the problem of deciding whether or not the distance is 0 is graph isomorphism complete but can be solved in polynomial time if the maximum outdegree of input trees is bounded by a constant. We also present parameterized and exponential-time algorithms for ordered and unordered cases, respectively

An approximate search engine for structure

As the size of structural databases grows, the need for efficiently searching these databases arises. Thanks to previous and ongoing research, searching by attribute-value and by text has become commonplace in these databases. However, searching by topological or physical structure, especially for large databases and especially for approximate matches, is still an art. In this dissertation, efficient search techniques are presented for retrieving trees from a database that are similar to a given query tree. Rooted ordered labeled trees, rooted unordered labeled trees and free trees are considered. Ordered labeled trees are trees in which each node has a label and the left-to-right order among siblings matters. Unordered labeled trees are trees in which the parent-child relationship is significant, but the order among siblings is unimportant. Free trees (unrooted unordered trees) are acyclic graphs. These trees find many applications in bioinformatics, Web log analysis, phyloinformatics, XML processing, etc. Two types of similarity measures are investigated: (i) counting the mismatching paths in the query tree and a data tree, and (ii) measuring the topological relationship between the trees. The proposed approaches include storing the paths of trees in a suffix array, employing hashing techniques to speed up retrieval, and counting the number of up-down operations to move a token from one node to another node in a tree. Various filters for accelerating a search, different strategies for parallelizing these search algorithms and applications of these algorithms to XML and phylogenetic data management are discussed. The proposed techniques have been implemented into a phylogenetic search engine which is fully operational and is available on the World Wide Web. Experimental results on comparing the similarity measures with existing tree metrics and on evaluating the efficiency of the search techniques demonstrate the effectiveness of the search engine. Future work includes extending the techniques to other structural data, as well as developing new filters and algorithms for speeding up searching and mining in complex structures

A Multi-labeled Tree Edit Distance for Comparing "Clonal Trees" of Tumor Progression

We introduce a new edit distance measure between a pair of "clonal trees", each representing the progression and mutational heterogeneity of a tumor sample, constructed by the use of single cell or bulk high throughput sequencing data. In a clonal tree, each vertex represents a specific tumor clone, and is labeled with one or more mutations in a way that each mutation is assigned to the oldest clone that harbors it. Given two clonal trees, our multi-labeled tree edit distance (MLTED) measure is defined as the minimum number of mutation/label deletions, (empty) leaf deletions, and vertex (clonal) expansions, applied in any order, to convert each of the two trees to the maximal common tree. We show that the MLTED measure can be computed efficiently in polynomial time and it captures the similarity between trees of different clonal granularity well. We have implemented our algorithm to compute MLTED exactly and applied it to a variety of data sets successfully. The source code of our method can be found in: https://github.com/khaled-rahman/leafDelTED

A survey on tree matching and XML retrieval

International audienceWith the increasing number of available XML documents, numerous approaches for retrieval have been proposed in the literature. They usually use the tree representation of documents and queries to process them, whether in an implicit or explicit way. Although retrieving XML documents can be considered as a tree matching problem between the query tree and the document trees, only a few approaches take advantage of the algorithms and methods proposed by the graph theory. In this paper, we aim at studying the theoretical approaches proposed in the literature for tree matching and at seeing how these approaches have been adapted to XML querying and retrieval, from both an exact and an approximate matching perspective. This study will allow us to highlight theoretical aspects of graph theory that have not been yet explored in XML retrieval