Comparing similar ordered trees in linear-time

AbstractWe describe a linear-time algorithm for comparing two similar ordered rooted trees with node labels. The method for comparing trees is the usual tree edit distance. We show that an optimal mapping that uses at most k insertions or deletions can then be constructed in O(nk3) where n is the size of the trees. The approach is inspired by the Zhang–Shasha algorithm for tree edit distance in combination with an adequate pruning of the search space based on the tree edit graph

Automatic Wrapper Adaptation by Tree Edit Distance Matching

Information distributed through the Web keeps growing faster day by day,\ud and for this reason, several techniques for extracting Web data have been suggested\ud during last years. Often, extraction tasks are performed through so called wrappers,\ud procedures extracting information from Web pages, e.g. implementing logic-based\ud techniques. Many fields of application today require a strong degree of robustness\ud of wrappers, in order not to compromise assets of information or reliability of data\ud extracted.\ud Unfortunately, wrappers may fail in the task of extracting data from a Web page, if\ud its structure changes, sometimes even slightly, thus requiring the exploiting of new\ud techniques to be automatically held so as to adapt the wrapper to the new structure\ud of the page, in case of failure. In this work we present a novel approach of automatic wrapper adaptation based on the measurement of similarity of trees through\ud improved tree edit distance matching techniques

Efficient chaining of seeds in ordered trees

We consider here the problem of chaining seeds in ordered trees. Seeds are mappings between two trees Q and T and a chain is a subset of non overlapping seeds that is consistent with respect to postfix order and ancestrality. This problem is a natural extension of a similar problem for sequences, and has applications in computational biology, such as mining a database of RNA secondary structures. For the chaining problem with a set of m constant size seeds, we describe an algorithm with complexity O(m2 log(m)) in time and O(m2) in space

Tree Edit Distance Learning via Adaptive Symbol Embeddings

Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as molecular structures, abstract syntax trees of computer programs, or syntax trees of natural language, by learning the cost function of an edit distance, i.e. the costs of replacing, deleting, or inserting nodes in a tree. However, learning such costs directly may yield an edit distance which violates metric axioms, is challenging to interpret, and may not generalize well. In this contribution, we propose a novel metric learning approach for trees which we call embedding edit distance learning (BEDL) and which learns an edit distance indirectly by embedding the tree nodes as vectors, such that the Euclidean distance between those vectors supports class discrimination. We learn such embeddings by reducing the distance to prototypical trees from the same class and increasing the distance to prototypical trees from different classes. In our experiments, we show that BEDL improves upon the state-of-the-art in metric learning for trees on six benchmark data sets, ranging from computer science over biomedical data to a natural-language processing data set containing over 300,000 nodes.Comment: Paper at the International Conference of Machine Learning (2018), 2018-07-10 to 2018-07-15 in Stockholm, Swede

Longest Common Pattern between two Permutations

In this paper, we give a polynomial (O(n^8)) algorithm for finding a longest common pattern between two permutations of size n given that one is separable. We also give an algorithm for general permutations whose complexity depends on the length of the longest simple permutation involved in one of our permutations