Ana Graça

Efficient haplotype inference with pseudo-boolean optimization

Haplotype inference from genotype data is a key computational problem in bioinformatics, since retrieving directly haplotype information from DNA samples is not feasible using existing technology. One of the methods for solving this problem uses the pure parsimony criterion, an approach known as Haplotype Inference by Pure Parsimony (HIPP). Initial work in this area was based on a number of different Integer Linear Programming (ILP) models and branch and bound algorithms. Recent work has shown that the utilization of a Boolean Satisfiability (SAT) formulation and state of the art SAT solvers represents the most efficient approach for solving the HIPP problem. Motivated by the promising results obtained using SAT techniques, this paper investigates the utilization of modern Pseudo-Boolean Optimization (PBO) algorithms for solving the HIPP problem. The paper starts by applying PBO to existing ILP models. The results are promising, and motivate the development of a new PBO model (RPoly) for the HIPP problem, which has a compact representation and eliminates key symmetries. Experimental results indicate that RPoly outperforms the SAT-based approach on most problem instances, being, in general, significantly more efficient.

Boolean lexicographic optimization: algorithms & applications

Multi-Objective Combinatorial Optimization (MOCO) problems find a wide range of practical application problems, some of which involving Boolean variables and constraints. This paper develops and evaluates algorithms for solving MOCO problems, defined on Boolean domains, and where the optimality criterion is lexicographic. The proposed algorithms build on existing algorithms for either Maximum Satisfiability (MaxSAT), Pseudo-Boolean Optimization (PBO), or Integer Linear Programming (ILP). Experimental results, obtained on problem instances from haplotyping with pedigrees and software package dependencies, show that the proposed algorithms can provide significant performance gains over state of the art MaxSAT, PBO and ILP algorithms. Finally, the paper also shows that lexicographic optimization conditions are observed in the majority of the problem instances from the MaxSAT evaluations, motivating the development of dedicated algorithms that can exploit lexicographic optimization conditions in general MaxSAT problem instances.

Efficient and accurate haplotype inference by combining parsimony and pedigree information

Existing genotyping technologies have enabled researchers to genotype hundreds of thousands of SNPs efficiently and inexpensively. Methods for the imputation of non-genotyped SNPs and the inference of haplotype information from genotypes, however, remain important, since they have the potential to increase the power of statistical association tests. In many cases, studies are conducted in sets of individuals where the pedigree information is relevant, and can be used to increase the power of tests and to decrease the impact of population structure on the obtained results. This paper proposes a new Boolean optimization model for haplotype inference combining two combinatorial approaches: the Minimum Recombinant Haplotyping Configuration (MRHC), which minimizes the number of recombinant events within a pedigree, and the Haplotype Inference by Pure Parsimony (HIPP), that aims at finding a solution with a minimum number of distinct haplotypes within a population. The paper also describes the use of well-known techniques, which yield significant performance gains. Concrete examples include symmetry breaking, identification of lower bounds, and the use of an appropriate constraint solver. Experimental results show that the new PedRPoly model is competitive both in terms of accuracy and efficiency.

Efficient haplotype inference with combined CP and OR techniques

Haplotype inference has relevant biological applications, and represents a challenging computational problem. Among others, pure parsimony provides a viable modeling approach for haplotype inference and provides a simple optimization criterion. Alternative approaches have been proposed for haplotype inference by pure parsimony (HIPP), including branch and bound, integer programming and, more recently, propositional satisfiability and pseudo-Boolean optimization (PBO). Among these, the currently best performing HIPP approach is based on PBO. This paper proposes a number of effective improvements to PBO-based HIPP, including the use of lower bounding and pruning techniques effective with other approaches. The new PBO-based HIPP approach reduces by 50% the number of instances that remain unsolvable by HIPP based approaches.

Haplotype Inference by Pure Parsimony: A Survey

Given a set of genotypes from a population, the process of recovering the haplotypes that explain the genotypes is called haplotype inference. The haplotype inference problem under the assumption of pure parsimony consists in finding the smallest number of haplotypes that explain a given set of genotypes. This problem is NP-hard. The original formulations for solving the Haplotype Inference by Pure Parsimony (HIPP) problem were based on integer linear programming and branch-and-bound techniques. More recently, solutions based on Boolean satisfiability, pseudo-Boolean optimization, and answer set programming have been shown to be remarkably more efficient. HIPP can now be regarded as a feasible approach for haplotype inference, which can be competitive with other different approaches. This article provides an overview of the methods for solving the HIPP problem, including preprocessing, bounding techniques, and heuristic approaches. The article also presents an empirical evaluation of exact HIPP solvers on a comprehensive set of synthetic and real problem instances. Moreover, the bounding techniques to the exact problem are evaluated. The final section compares and discusses the HIPP approach with a well-established statistical method that represents the reference algorithm for this problem.

Efficient and tight upper bounds for haplotype inference by pure parsimony using delayed haplotype selection

Haplotype inference from genotype data is a key step towards a better understanding of the role played by genetic variations on inherited diseases. One of the most promising approaches uses the pure parsimony criterion. This approach is called Haplotype Inference by Pure Parsimony (HIPP) and is NP-hard as it aims at minimising the number of haplotypes required to explain a given set of genotypes. The HIPP problem is often solved using constraint satisfaction techniques, for which the upper bound on the number of required haplotypes is a key issue. Another very well-known approach is Clarks method, which resolves genotypes by greedily selecting an explaining pair of haplotypes. In this work, we combine the basic idea of Clarks method with a more sophisticated method for the selection of explaining haplotypes, in order to explicitly introduce a bias towards parsimonious explanations. This new algorithm can be used either to obtain an approximated solution to the HIPP problem or to obtain an upper bound on the size of the pure parsimony solution. This upper bound can then used to efficiently encode the problem as a constraint satisfaction problem. The experimental evaluation, conducted using a large set of real and artificially generated examples, shows that the new method is much more effective than Clarks method at obtaining parsimonious solutions, while keeping the advantages of simplicity and speed of Clarks method.

Haplotype Inference with Boolean Constraint Solving: An Overview

Boolean satisfiability (SAT) finds a wide range of practical applications, including Artificial Intelligence and, more recently, Bioinformatics. Although encoding some combinatorial problems using Boolean logic may not be the most intuitive solution, the efficiency of state-of-the-art SAT solvers often makes it worthwhile to consider encoding a problem to SAT. One representative application of SAT in Bioinformatics is haplotype inference. The problem of haplotype inference under the assumption of pure parsimony consists in finding the smallest number of haplotypes that explains a given set of genotypes. The original formulations for solving the problem of Haplotype Inference by Pure Parsimony (HIPP) were based on Integer Linear Programming. More recently, solutions based on SAT have been shown to be remarkably more efficient. This paper provides an overview of SAT-based approaches for solving the HIPP problem and identifies current research directions.

Haplotype Inference Using Propositional Satisfiability

Haplotype inference is an important problem in computational biology, which has deserved large effort and attention in the recent years. Haplotypes encode the genetic data of an individual at a single chromosome. However, humans are diploid (chromosomes have maternal and paternal origin), and it is technologically infeasible to separate the information from homologous chromosomes. Hence, mathematical methods are required to solve the haplotype inference problem. A relevant approach is the pure parsimony. The haplotype inference by pure parsimony (HIPP) aims at finding the minimum number of haplotypes which explains a given set of genotypes. This problem is NP-hard. Boolean satisfiability (SAT) has successful applications in several fields. The use of SAT-based techniques with pure parsimony haplotyping has shown to produce very efficient results. This chapter describes the haplotype inference problem and the SAT-based models developed to solve the problem. Experimental results confirm that the SAT-based methods represent the state of the art in the field of HIPP.