arXiv subjects

Paola Bonizzoni

Publications and source records attributed to Paola Bonizzoni.

35 records · Page 2Linked to original sources

arXiv2016

A New Lightweight Algorithm to compute the BWT and the LCP array of a Set of Strings

Indexing of very large collections of strings such as those produced by the widespread sequencing technologies, heavily relies on multi-string generalizations of the Burrows-Wheeler Transform (BWT), and for this problem various in-memory algorithms have been proposed. The rapid growing of data that are processed routinely, such as in bioinformatics, requires a large amount of main memory, and this fact has motivated the development of algorithms, to compute the BWT, that work almost entirely in external memory. On the other hand, the related problem of computing the Longest Common Prefix (LCP) array is often instrumental in several algorithms on collection of strings, such as those that compute the suffix-prefix overlap among strings, which is an essential step for many genome assembly algorithms. The best current lightweight approach to compute BWT and LCP array on a set of $m$ strings, each one $k$ characters long, has I/O complexity that is $O(mk^2 \log |Σ|)$ (where $|Σ|$ is the size of the alphabet), thus it is not optimal. In this paper we propose a novel approach to build BWT and LCP array (simultaneously) with $O(kmL(\log k +\log σ))$ I/O complexity, where $L$ is the length of longest substring that appears at least twice in the input strings.

cs.DS↗

arXiv2015

Splicing Systems from Past to Future: Old and New Challenges

A splicing system is a formal model of a recombinant behaviour of sets of double stranded DNA molecules when acted on by restriction enzymes and ligase. In this survey we will concentrate on a specific behaviour of a type of splicing systems, introduced by Păun and subsequently developed by many researchers in both linear and circular case of splicing definition. In particular, we will present recent results on this topic and how they stimulate new challenging investigations.

cs.FL↗

arXiv2015

An External-Memory Algorithm for String Graph Construction

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.

cs.DS↗

arXiv2014

Algorithms for the Constrained Perfect Phylogeny with Persistent Characters

The perfect phylogeny is one of the most used models in different areas of computational biology. In this paper we consider the problem of the Persistent Perfect Phylogeny (referred as P-PP) recently introduced to extend the perfect phylogeny model allowing persistent characters, that is characters can be gained and lost at most once. We define a natural generalization of the P-PP problem obtained by requiring that for some pairs (character, species), neither the species nor any of its ancestors can have the character. In other words, some characters cannot be persistent for some species. This new problem is called Constrained P-PP (CP-PP). Based on a graph formulation of the CP-PP problem, we are able to provide a polynomial time solution for the CP-PP problem for matrices having an empty conflict-graph. In particular we show that all such matrices admit a persistent perfect phylogeny in the unconstrained case. Using this result, we develop a parameterized algorithm for solving the CP-PP problem where the parameter is the number of characters. A preliminary experimental analysis of the algorithm shows that it performs efficiently and it may analyze real haplotype data not conforming to the classical perfect phylogeny model.

cs.DS↗

arXiv2013

Covering Pairs in Directed Acyclic Graphs

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.

cs.DS↗

arXiv2012

Reconstructing Isoform Graphs from RNA-Seq data

Next-generation sequencing (NGS) technologies allow new methodologies for alternative splicing (AS) analysis. Current computational methods for AS from NGS data are mainly focused on predicting splice site junctions or de novo assembly of full-length transcripts. These methods are computationally expensive and produce a huge number of full-length transcripts or splice junctions, spanning the whole genome of organisms. Thus summarizing such data into the different gene structures and AS events of the expressed genes is an hard task. To face this issue in this paper we investigate the computational problem of reconstructing from NGS data, in absence of the genome, a gene structure for each gene that is represented by the isoform graph: we introduce such graph and we show that it uniquely summarizes the gene transcripts. We define the computational problem of reconstructing the isoform graph and provide some conditions that must be met to allow such reconstruction. Finally, we describe an efficient algorithmic approach to solve this problem, validating our approach with both a theoretical and an experimental analysis.

q-bio.GN↗

arXiv2012

The Binary Perfect Phylogeny with Persistent characters

The binary perfect phylogeny model is too restrictive to model biological events such as back mutations. In this paper we consider a natural generalization of the model that allows a special type of back mutation. We investigate the problem of reconstructing a near perfect phylogeny over a binary set of characters where characters are persistent: characters can be gained and lost at most once. Based on this notion, we define the problem of the Persistent Perfect Phylogeny (referred as P-PP). We restate the P-PP problem as a special case of the Incomplete Directed Perfect Phylogeny, called Incomplete Perfect Phylogeny with Persistent Completion, (refereed as IP-PP), where the instance is an incomplete binary matrix M having some missing entries, denoted by symbol ?, that must be determined (or completed) as 0 or 1 so that M admits a binary perfect phylogeny. We show that the IP-PP problem can be reduced to a problem over an edge colored graph since the completion of each column of the input matrix can be represented by a graph operation. Based on this graph formulation, we develop an exact algorithm for solving the P-PP problem that is exponential in the number of characters and polynomial in the number of species.

cs.DS↗

arXiv2012

A Unifying Framework to Characterize the Power of a Language to Express Relations

In this extended abstract we provide a unifying framework that can be used to characterize and compare the expressive power of query languages for different data base models. The framework is based upon the new idea of valid partition, that is a partition of the elements of a given data base, where each class of the partition is composed by elements that cannot be separated (distinguished) according to some level of information contained in the data base. We describe two applications of this new framework, first by deriving a new syntactic characterization of the expressive power of relational algebra which is equivalent to the one given by Paredaens, and subsequently by studying the expressive power of a simple graph-based data model.

cs.DB↗

arXiv2011

Haplotype Inference on Pedigrees with Recombinations, Errors, and Missing Genotypes via SAT solvers

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.

cs.DS↗

arXiv2010

Parameterized Complexity of the k-anonymity Problem

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.

cs.DS↗

arXiv2010

PIntron: a Fast Method for Gene Structure Prediction via Maximal Pairings of a Pattern and a Text

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.

q-bio.GN↗

arXiv2010

Pure Parsimony Xor Haplotyping

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.

cs.CE↗

arXiv2009

Variants of Constrained Longest Common Subsequence

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.

cs.DS↗

arXiv2009

Circular Languages Generated by Complete Splicing Systems and Pure Unitary Languages

Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a characterization of the class of circular languages generated by circular splicing systems is still an open problem. In this paper we solve this problem for complete systems, which are special finite circular splicing systems. We show that a circular language L is generated by a complete system if and only if the set Lin(L) of all words corresponding to L is a pure unitary language generated by a set closed under the conjugacy relation. The class of pure unitary languages was introduced by A. Ehrenfeucht, D. Haussler, G. Rozenberg in 1983, as a subclass of the class of context-free languages, together with a characterization of regular pure unitary languages by means of a decidable property. As a direct consequence, we characterize (regular) circular languages generated by complete systems. We can also decide whether the language generated by a complete system is regular. Finally, we point out that complete systems have the same computational power as finite simple systems, an easy type of circular splicing system defined in the literature from the very beginning, when only one rule is allowed. From our results on complete systems, it follows that finite simple systems generate a class of context-free languages containing non-regular languages, showing the incorrectness of a longstanding result on simple systems.

cs.FL↗

arXiv2009

A PTAS for the Minimum Consensus Clustering Problem with a Fixed Number of Clusters

The Consensus Clustering problem has been introduced as an effective way to analyze the results of different microarray experiments. The problem consists of looking for a partition that best summarizes a set of input partitions (each corresponding to a different microarray experiment) under a simple and intuitive cost function. The problem admits polynomial time algorithms on two input partitions, but is APX-hard on three input partitions. We investigate the restriction of Consensus Clustering when the output partition is required to contain at most k sets, giving a polynomial time approximation scheme (PTAS) while proving the NP-hardness of this restriction.

cs.DS↗

arXiv2009

The $k$-anonymity Problem is Hard

The problem of publishing personal data without giving up privacy is becoming increasingly important. An interesting formalization recently proposed is the k-anonymity. This approach requires that the rows in a table are clustered in sets of size at least k and that all the rows in a cluster become the same tuple, after the suppression of some records. The natural optimization problem, where the goal is to minimize the number of suppressed entries, is known to be NP-hard when the values are over a ternary alphabet, k = 3 and the rows length is unbounded. In this paper we give a lower bound on the approximation factor that any polynomial-time algorithm can achive on two restrictions of the problem,namely (i) when the records values are over a binary alphabet and k = 3, and (ii) when the records have length at most 8 and k = 4, showing that these restrictions of the problem are APX-hard.

cs.DB↗

arXiv2005

Approximating Clustering of Fingerprint Vectors with Missing Values

The problem of clustering fingerprint vectors is an interesting problem in Computational Biology that has been proposed in (Figureroa et al. 2004). In this paper we show some improvements in closing the gaps between the known lower bounds and upper bounds on the approximability of some variants of the biological problem. Namely we are able to prove that the problem is APX-hard even when each fingerprint contains only two unknown position. Moreover we have studied some variants of the orginal problem, and we give two 2-approximation algorithm for the IECMV and OECMV problems when the number of unknown entries for each vector is at most a constant.

cs.DS↗