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We study the design of efficient algorithms for combinatorial pattern matching. More concretely, we study algorithms for tree matching, string matching, and string matching in compressed texts.
Approximate pattern matching is a natural and well-studied problem on strings: Given a text $T$, a pattern $P$, and a threshold $k$, find (the starting positions of) all substrings of $T$ that are at distance at most $k$ from $P$. We…
Tree matching techniques have been investigated in many fields, including web data mining and extraction, as a key component to analyze the content of web documents, existing tree matching approaches, like Tree-Edit Distance (TED) or…
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…
In this work, we address the problem of approximate pattern matching with wildcards. Given a pattern $P$ of length $m$ containing $D$ wildcards, a text $T$ of length $n$, and an integer $k$, our objective is to identify all fragments of $T$…
We present an efficient algorithm for finding all approximate occurrences of a given pattern $p$ of length $m$ in a text $t$ of length $n$ allowing for translocations of equal length adjacent factors and inversions of factors. The algorithm…
The goal of this paper is to study the similarity between sequences using a distance between the \emph{context} trees associated to the sequences. These trees are defined in the framework of \emph{Sparse Probabilistic Suffix Trees} (SPST),…
This paper presents a detailed comparison of a recently proposed algorithm for optimizing decision trees, tree alternating optimization (TAO), with other popular, established algorithms. We compare their performance on a number of…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
It is an open question whether there exists a polynomial-time algorithm for computing the rotation distances between pairs of extended ordered binary trees. The problem of computing the rotation distance between an arbitrary pair of trees,…
We present an online algorithm to deal with pattern matching in strings. The problem we investigate is commonly known as string matching with mismatches in which the objective is to report the number of characters that match when a pattern…
Finding an optimal assignment between two sets of objects is a fundamental problem arising in many applications, including the matching of `bag-of-words' representations in natural language processing and computer vision. Solving the…
We present four novel approximation algorithms for finding triangulation of minimum treewidth. Two of the algorithms improve on the running times of algorithms by Robertson and Seymour, and Becker and Geiger that approximate the optimum by…
We present a new efficient method for approximate search in electronic lexica. Given an input string (the pattern) and a similarity threshold, the algorithm retrieves all entries of the lexicon that are sufficiently similar to the pattern.…
Explaining why and how a tree $t$ structurally differs from another tree $t^\star$ is a question that is encountered throughout computer science, including in understanding tree-structured data such as XML or JSON data. In this article, we…
We propose a novel technique, termed compact shape trees, for computing correspondences of single-boundary 2-D shapes in O(n2) time. Together with zero or more features defined at each of n sample points on the shape's boundary, the compact…
Ancestral mixture model, proposed by Chen and Lindsay (2006), is an important model to build a hierarchical tree from high dimensional binary sequences. Mixture trees created from ancestral mixture models involve in the inferred…
A merge tree is a fundamental topological structure used to capture the sub-level set (and similarly, super-level set) topology in scalar data analysis. The interleaving distance is a theoretically sound, stable metric for comparing merge…
Text-to-pattern distance is a fundamental problem in string matching, where given a pattern of length $m$ and a text of length $n$, over an integer alphabet, we are asked to compute the distance between pattern and the text at every…
Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape"…