Juan Mendivelso

δ γ --- Parameterized Matching

This paper defines a new pattern matching problem by combiningtwo paradigms: Δ γ ---matching andparameterized matching. The solution is essentially obtained by acombination of bitparallel techniques and a reduction to a graphmatching problem. The time complexity of the algorithm isO (nm ), assuming text size n , patternsize m and a constant size alphabet.

Solving Graph Isomorphism Using Parameterized Matching

We propose a new approach to solve graph isomorphism using parameterized matching. To find isomorphism between two graphs, one graph is linearized, i.e., represented as a graph walk that covers all nodes and edges such that each element is represented by a parameter. Next, we match the graph linearization on the second graph, searching for a bijective function that maps each element of the first graph to an element of the second graph. We develop an efficient linearization algorithm that generates short linearization with an approximation guarantee, and develop a graph matching algorithm. We evaluate our approach experimentally on graphs of different types and sizes, and compare to the performance of VF2, which is a prominent algorithm for graph isomorphism. Our empirical measurements show that graph linearization finds a matching graph faster than VF2 in many cases because of better pruning of the search space.

Approximate function matching under δ- and γ- distances

This paper defines a new string matching problem by combining two paradigms: function matching and δγ-matching. The result is an approximate variant of function matching where two equal-length strings X and Y match if there exists a function that maps X to a string X′ such that X′ and Y are δγ- similar. We propose an O(nm) algorithm for finding all the matches of a pattern P1 …m in a text T1 …n.

Finding overlaps within regular expressions with variable-length gaps

Regular expressions play an important role in various fields in computer science. However, handling many regular expressions in parallel requires huge computation resources. Therefore, it is necessary to find and eliminate overlapping regular expressions. In this paper, we consider a special type of regular expressions: expressions comprised of characters and variable-length gaps between such characters. Specifically, we propose a bit-parallel solution to determine whether the languages of two expressions <i>X</i> and <i>Y</i> with variable-length gaps have a common string. The time complexity of our algorithm is <i>O</i> (min (<i>L</i>_<i>X</i> ²|Σ|, <i>L</i>_<i>X</i> <i>L</i>_<i>Y</i>)/<i>w</i>) where Σ is the alphabet from which <i>X</i> and <i>Y</i> are drawn, <i>L</i>_<i>X</i> and <i>L</i>_<i>Y</i> are the lengths of the longest strings that respectively match <i>X</i> and <i>Y</i>, and <i>w</i> is the size of the computer word.

A multiobjective optimization algorithm for the weighted LCS

Computing a similarity measure of a given set of molecular sequences is an important task in bioinformatics studies. Weighted sequences have become an interesting research area since they allow a newer and more precise encoding paradigm of molecular structures. The longest common subsequence (LCS) has been an extensively studied technique to compute similarity on sequences represented as strings and it has been used in many applications. There is a current trend to generalize those algorithms to work on weighted sequences too. The resulting variant of the problem is called the weighted LCS. In this paper, we study the problem of finding the weighted LCS of two weighted sequences. Particularly, a novel approach is presented to tackle the weighted LCS for a bounded molecular alphabet constrained by one or two α parameters. Based on the dominant-match-point paradigm, we model the problem using a multiobjective optimization approach. As a result, we propose a novel, efficient and exact algorithm that not only finds the weighted LCS but also the set of all possible solutions. We perform experimental analysis using simulated and real data to compare the performance of the proposed approach. The experiments show that the proposed algorithm has a good performance in small instances of both benchmarks. Furthermore, it can be used on a great number of bioinformatics applications where the computation of similarity between short sequence fragments is needed.

Approximate Abelian Periods to Find Motifs in Biological Sequences

A problem that has been gaining importance in recent years is that of computing the Abelian periods in a string. A string w has an Abelian period p if it is a sequence of permutations of a length–p string. In this paper, we define an approximate variant of Abelian periods which allows variations between adjacent elements of the sequence. Particularly, we compare two adjacent elements in the sequence using δ– and γ– metrics. We develop an algorithm for computing all the δγ–approximate Abelian periods in a string under two proposed definitions. We also show a preliminary application to the problem of identifying genes with periodic variations in their expression levels.

Segment and Fenwick Trees for Approximate Order Preserving Matching

In this paper we combine two string searching related problems: the approximate string matching under parameters \(\delta \) and \(\gamma \), and the order preserving matching problem. Order-preserving matching regards the internal structure of the strings rather than their absolute values while matching under \(\delta \) and \(\gamma \) distances permit a level of error. We formally define the \(\delta \gamma \)–order-preserving matching problem. We designed two algorithms for it based on the segment tree and the Fenwick tree, respectively. Also, we design and implement in C++ and an experimental setup to compare these algorithms with the naive solution and the updateBA algorithm introduced in [22]. The data structure based algorithms show better experimental performance due to their better lower bound of \(\varOmega (n \lg n)\) complexity.