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Feature embedding methods have been proposed in literature to represent sequences as numeric vectors to be used in some bioinformatics investigations, such as family classification and protein structure prediction. Recent theoretical results showed that the well-known Lyndon factorization preserves common factors in overlapping strings. Surprisingly, the fingerprint of a sequencing read, which is the sequence of lengths of consecutive factors in variants of the Lyndon factorization of the read, is effective in preserving sequence similarities, suggesting it as basis for the definition of novels representations of sequencing reads. We propose a novel feature embedding method for Next-Generation Sequencing (NGS) data using the notion of fingerprint. We provide a theoretical and experimental framework to estimate the behaviour of fingerprints and of the $k$-mers extracted from it, called $k$-fingers, as possible feature embeddings for sequencing reads. As a case study to assess the effectiveness of such embeddings, we use fingerprints to represent RNA-Seq reads and to assign them to the most likely gene from which they were originated as fragments of transcripts of the gene. We provide an implementation of the proposed method in the tool lyn2vec, which produces Lyndon-based feature embeddings of sequencing reads.

Indexing very large collections of strings, such as those produced by the widespread next generation sequencing technologies, heavily relies on multistring generalization of the Burrows-Wheeler Transform (BWT): large requirements of in-memory approaches have stimulated recent developments on external memory algorithms. The related problem of computing the Longest Common Prefix (LCP) array of a set of strings is instrumental to compute the suffix-prefix overlaps among strings, which is an essential step for many genome assembly algorithms. In a previous paper, we presented an in-memory divide-and-conquer method for building the BWT and LCP where we merge partial BWTs with a forward approach to sort suffixes. In this paper, we propose an alternative backward strategy to develop an external memory method to simultaneously build the BWT and the LCP array on a collection of m strings of different lengths. The algorithm over a set of strings having constant length k has O(mkl) time and I/O volume, using O(k + m) main memory, where l is the maximum value in the LCP array., Comment: Theoretical Computer Science (2020). arXiv admin note: text overlap with arXiv:1607.08342

The string graph for a collection of next-generation reads is a lossless data representation that is fundamental for de novo assemblers based on the overlap-layout-consensus paradigm. In this paper, we explore a novel approach to compute the string graph, based on the FM-index and Burrows-Wheeler Transform. We describe a simple algorithm that uses only the FM-index representation of the collection of reads to construct the string graph, without accessing the input reads. Our algorithm has been integrated into the SGA assembler as a standalone module to construct the string graph. The new integrated assembler has been assessed on a standard benchmark, showing that FSG is significantly faster than SGA while maintaining a moderate use of main memory, and showing practical advantages in running FSG on multiple threads., Comment: Accepted to Journal of Computational Biology

Some recent results have introduced external-memory algorithms to compute self-indexes of a set of strings, mainly via computing the Burrows-Wheeler Transform (BWT) of the input strings. The motivations for those results stem from Bioinformatics, where a large number of short strings (called reads) are routinely produced and analyzed. In that field, a fundamental problem is to assemble a genome from a large set of much shorter samples extracted from the unknown genome. The approaches that are currently used to tackle this problem are memory-intensive. This fact does not bode well with the ongoing increase in the availability of genomic data. A data structure that is used in genome assembly is the string graph, where vertices correspond to samples and arcs represent two overlapping samples. In this paper we address an open problem: to design an external-memory algorithm to compute the string graph.

The Minimum Path Cover problem on directed acyclic graphs (DAGs) is a classical problem that provides a clear and simple mathematical formulation for several applications in different areas and that has an efficient algorithmic solution. In this paper, we study the computational complexity of two constrained variants of Minimum Path Cover motivated by the recent introduction of next-generation sequencing technologies in bioinformatics. The first problem (MinPCRP), given a DAG and a set of pairs of vertices, asks for a minimum cardinality set of paths "covering" all the vertices such that both vertices of each pair belong to the same path. For this problem, we show that, while it is NP-hard to compute if there exists a solution consisting of at most three paths, it is possible to decide in polynomial time whether a solution consisting of at most two paths exists. The second problem (MaxRPSP), given a DAG and a set of pairs of vertices, asks for a path containing the maximum number of the given pairs of vertices. We show its NP-hardness and also its W[1]-hardness when parametrized by the number of covered pairs. On the positive side, we give a fixed-parameter algorithm when the parameter is the maximum overlapping degree, a natural parameter in the bioinformatics applications of the problem.

The Minimum-Recombinant Haplotype Configuration problem (MRHC) has been highly successful in providing a sound combinatorial formulation for the important problem of genotype phasing on pedigrees. Despite several algorithmic advances and refinements that led to some efficient algorithms, its applicability to real datasets has been limited by the absence of some important characteristics of these data in its formulation, such as mutations, genotyping errors, and missing data. In this work, we propose the Haplotype Configuration with Recombinations and Errors problem (HCRE), which generalizes the original MRHC formulation by incorporating the two most common characteristics of real data: errors and missing genotypes (including untyped individuals). Although HCRE is computationally hard, we propose an exact algorithm for the problem based on a reduction to the well-known Satisfiability problem. Our reduction exploits recent progresses in the constraint programming literature and, combined with the use of state-of-the-art SAT solvers, provides a practical solution for the HCRE problem. Biological soundness of the phasing model and effectiveness (on both accuracy and performance) of the algorithm are experimentally demonstrated under several simulated scenarios and on a real dairy cattle population., Comment: 14 pages, 1 figure, 4 tables, the associated software reHCstar is available at http://www.algolab.eu/reHCstar

Current computational methods for exon-intron structure prediction from a cluster of transcript (EST, mRNA) data do not exhibit the time and space efficiency necessary to process large clusters of over than 20,000 ESTs and genes longer than 1Mb. Guaranteeing both accuracy and efficiency seems to be a computational goal quite far to be achieved, since accuracy is strictly related to exploiting the inherent redundancy of information present in a large cluster. We propose a fast method for the problem that combines two ideas: a novel algorithm of proved small time complexity for computing spliced alignments of a transcript against a genome, and an efficient algorithm that exploits the inherent redundancy of information in a cluster of transcripts to select, among all possible factorizations of EST sequences, those allowing to infer splice site junctions that are highly confirmed by the input data. The EST alignment procedure is based on the construction of maximal embeddings that are sequences obtained from paths of a graph structure, called Embedding Graph, whose vertices are the maximal pairings of a genomic sequence T and an EST P. The procedure runs in time linear in the size of P, T and of the output. PIntron, the software tool implementing our methodology, is able to process in a few seconds some critical genes that are not manageable by other gene structure prediction tools. At the same time, PIntron exhibits high accuracy (sensitivity and specificity) when compared with ENCODE data. Detailed experimental data, additional results and PIntron software are available at http://www.algolab.eu/PIntron.

The haplotype resolution from xor-genotype data has been recently formulated as a new model for genetic studies. The xor-genotype data is a cheaply obtainable type of data distinguishing heterozygous from homozygous sites without identifying the homozygous alleles. In this paper we propose a formulation based on a well-known model used in haplotype inference: pure parsimony. We exhibit exact solutions of the problem by providing polynomial time algorithms for some restricted cases and a fixed-parameter algorithm for the general case. These results are based on some interesting combinatorial properties of a graph representation of the solutions. Furthermore, we show that the problem has a polynomial time k-approximation, where k is the maximum number of xor-genotypes containing a given SNP. Finally, we propose a heuristic and produce an experimental analysis showing that it scales to real-world large instances taken from the HapMap project.

In this work, we consider a variant of the classical Longest Common Subsequence problem called Doubly-Constrained Longest Common Subsequence (DC-LCS). Given two strings s1 and s2 over an alphabet A, a set C_s of strings, and a function Co from A to N, the DC-LCS problem consists in finding the longest subsequence s of s1 and s2 such that s is a supersequence of all the strings in Cs and such that the number of occurrences in s of each symbol a in A is upper bounded by Co(a). The DC-LCS problem provides a clear mathematical formulation of a sequence comparison problem in Computational Biology and generalizes two other constrained variants of the LCS problem: the Constrained LCS and the Repetition-Free LCS. We present two results for the DC-LCS problem. First, we illustrate a fixed-parameter algorithm where the parameter is the length of the solution. Secondly, we prove a parameterized hardness result for the Constrained LCS problem when the parameter is the number of the constraint strings and the size of the alphabet A. This hardness result also implies the parameterized hardness of the DC-LCS problem (with the same parameters) and its NP-hardness when the size of the alphabet is constant.

The problem of publishing personal data without giving up privacy is becoming increasingly important. An interesting formalization that has been recently proposed is the $k$-anonymity. This approach requires that the rows of a table are partitioned in clusters of size at least $k$ and that all the rows in a cluster become the same tuple, after the suppression of some entries. The natural optimization problem, where the goal is to minimize the number of suppressed entries, is known to be APX-hard even when the records values are over a binary alphabet and $k=3$, and when the records have length at most 8 and $k=4$ . In this paper we study how the complexity of the problem is influenced by different parameters. In this paper we follow this direction of research, first showing that the problem is W[1]-hard when parameterized by the size of the solution (and the value $k$). Then we exhibit a fixed parameter algorithm, when the problem is parameterized by the size of the alphabet and the number of columns. Finally, we investigate the computational (and approximation) complexity of the $k$-anonymity problem, when restricting the instance to records having length bounded by 3 and $k=3$. We show that such a restriction is APX-hard., Comment: 22 pages, 2 figures