- 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 single path containing the maximum number of the given pairs of vertices. We show its NP-hardness and also its W-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.
- Computational methods for gene allele prediction have been proposed to substitute dedicated and expensive assays with cheaper in-silico analyses that operate on routinely collected data, such as SNP genotypes. Most of these methods are tailored to the needs and characteristics of human genetic studies where they achieve good prediction accuracy. However, genomic analyses are becoming increasingly important in livestock species too. For livestock species generally the underlying—usually quite large and complex—pedigree is known and available; this information is not fully exploited by current allele prediction methods.
In this work, we propose a new gene allele prediction method based on a simple, but robust, combinatorial formulation for the problem of discovering haplotype-allele associations. The inherent uncertainty of the haplotype inference process is reduced by taking into account the inheritance of gene alleles across the population pedigree while genotypes are phased. The accuracy of the method has been extensively evaluated on a representative real-world livestock dataset under several scenarios and choices of parameters. The median error rate ranged from 0.0537 to 0.0896, with an average of 0.0678; this is 21% better than another state-of-the-art prediction algorithm that does not use the pedigree information. The experimental results support the validity of the proposed approach and, in particular, of the use of pedigree information in gene allele predictions.
- This work proposes the Min-Recombinant Haplotype Configuration with Bounded Errors problem (MRHCE), which extends the original Min-Recombinant Haplotype Configuration formulation by incorporating two common characteristics of real data: errors and missing genotypes (including untyped individuals). We describe a practical algorithm for MRHCE that is based on a reduction to the Satisfiability problem (SAT) and exploits recent advances in the constraint programming literature. An experimental analysis demonstrates the soundness of our model and the effectiveness of the algorithm under several scenarios. The analysis on real data and the comparison with state-of-the-art programs reveals that our approach couples better scalability to large and complex pedigrees with the explicit inclusion of genotyping errors into the model. The software, released under the GNU General Public License, can be freely downloaded from this page.
- In this work, we propose a novel pipeline for computational gene-structure prediction based on spliced alignment of expressed sequences (ESTs and mRNAs). This pipeline, called PIntron, is composed by four steps: Firstly, alternative alignments of expressed sequences to a reference genomic sequence are implicitly computed and represented in a graph (called embedding graph) by a novel fast spliced alignment procedure. Secondly, biologically meaningful alignments are extracted. Then, a consensus gene structure induced by the previously computed alignments is determined based on a parsimony principle. Finally, the resulting introns are reconciliated and classified according to general biological criteria. The software, released under the GNU Affero General Public License, can be freely downloaded from this page.
- The work proposes a new combinatorial formulation for haplotype inference on general pedigrees that generalizes the existing combinatorial ones to a more realistic settings. We prove an approximation-preserving reduction from this problem, called Minimum Change Haplotype Configuration (MCHC), to a well-known coding theory problem, namely the Nearest Codeword Problem. This reduction automatically implies the approximability of MCHC within a factor O(n/log n) and, more importantly, it leads to a new very efficient heuristic algorithm that has been experimentally compared with other state-of-the-art HI methods. The software implementing the heuristic is freely available at this page under the GNU General Public License.
- In this work we addressed the problem of haplotype inference from xor genotypes under the pure parsimony assumption. Exact algorithms for restricted instances, a fixed parameter algorithm, an approximation algorithm, and an effective heuristic have been proposed. A prototypical implementation of the heuristic is freely available at this page under the GNU General Public License.
- The work presents a new parsimony-based formulation for the problem of choosing the best alignment of an expressed sequence against a genomic sequence exploiting the redundancy of current expressed sequence databases. A preliminary experimental evaluation of the formulation and the related algorithm shows their applicability on real instances. The implementation of this approach is integrated in our software PIntron.