A three-phased local search approach for the clique partitioning problem

This paper presents a three-phased local search heuristic CPP-P3 for solving the Clique Partitioning Problem (CPP). CPP-P3 iterates a descent search, an exploration search and a directed perturbation. We also define the Top Move of a vertex, in order to build a restricted and focused neighborhood. The exploration search is ensured by a tabu procedure, while the directed perturbation uses a GRASP-like method. To assess the performance of the proposed approach, we carry out extensive experiments on benchmark instances of the literature as well as newly generated instances. We demonstrate the effectiveness of our approach with respect to the current best performing algorithms both in terms of solution quality and computation efficiency. We present improved best solutions for a number of benchmark instances. Additional analyses are shown to highlight the critical role of the Top Move-based neighborhood for the performance of our algorithm and the relation between instance hardness and algorithm behavior

A hierarchical Bayesian network approach for linkage disequilibrium modeling and data-dimensionality reduction prior to genome-wide association studies

<p>Abstract</p> <p>Background</p> <p>Discovering the genetic basis of common genetic diseases in the human genome represents a public health issue. However, the dimensionality of the genetic data (up to 1 million genetic markers) and its complexity make the statistical analysis a challenging task.</p> <p>Results</p> <p>We present an accurate modeling of dependences between genetic markers, based on a forest of hierarchical latent class models which is a particular class of probabilistic graphical models. This model offers an adapted framework to deal with the fuzzy nature of linkage disequilibrium blocks. In addition, the data dimensionality can be reduced through the latent variables of the model which synthesize the information borne by genetic markers. In order to tackle the learning of both forest structure and probability distributions, a generic algorithm has been proposed. A first implementation of our algorithm has been shown to be tractable on benchmarks describing 10⁵variables for 2000 individuals.</p> <p>Conclusions</p> <p>The forest of hierarchical latent class models offers several advantages for genome-wide association studies: accurate modeling of linkage disequilibrium, flexible data dimensionality reduction and biological meaning borne by latent variables.</p

Subnetwork Constraints for Tighter Upper Bounds and Exact Solution of the Clique Partitioning Problem

We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning problem, being NP-hard in the general case of having edge weights of different signs. We propose a new method of estimating an upper bound of the objective function that we combine with the classical branch-and-bound technique to find the exact solution. We evaluate our approach on a broad range of random graphs and real-world networks. The proposed approach provided tighter upper bounds and achieved significant convergence speed improvements compared to known alternative methods.Comment: 20 pages, 3 figure

A Parallel Direct Method for Finite Element Electromagnetic Computations Based on Domain Decomposition

High performance parallel computing and direct (factorization-based) solution methods have been the two main trends in electromagnetic computations in recent years. When time-harmonic (frequency-domain) Maxwell\u27s equation are directly discretized with the Finite Element Method (FEM) or other Partial Differential Equation (PDE) methods, the resulting linear system of equations is sparse and indefinite, thus harder to efficiently factorize serially or in parallel than alternative methods e.g. integral equation solutions, that result in dense linear systems. State-of-the-art sparse matrix direct solvers such as MUMPS and PARDISO don\u27t scale favorably, have low parallel efficiency and high memory footprint. This work introduces a new class of sparse direct solvers based on domain decomposition method, termed Direct Domain Decomposition Method (D3M), which is reliable, memory efficient, and offers very good parallel scalability for arbitrary 3D FEM problems. Unlike recent trends in approximate/low-rank solvers, this method focuses on `numerically exact\u27 solution methods as they are more reliable for complex `real-life\u27 models. The proposed method leverages physical insights at every stage of the development through a new symmetric domain decomposition method (DDM) with one set of Lagrange multipliers. Applying a special regularization scheme at the interfaces, either artificial loss or gain is introduced to each domain to eliminate non-physical internal resonances. A block-wise recursive algorithm based on Takahashi relationship is proposed for the efficient computation of discrete Dirichlet-to-Neumann (DtN) map to reduce the volumetric problem from all domains into an auxiliary surfacial problem defined on the domain interfaces only. Numerical results show up to 50% run-time saving in DtN map computation using the proposed block-wise recursive algorithm compared to alternative approaches. The auxiliary unknowns on the domain interfaces form a considerably (approximately an order of magnitude) smaller block-wise sparse matrix, which is efficiently factorized using a customized block LDL$^T$ factorization with restricted pivoting to ensure stability. The parallelization of the proposed D3M is realized based on Directed Acyclic Graph (DAG). Recent advances in parallel dense direct solvers, have shifted toward parallel implementation that rely on DAG scheduling to achieve highly efficient asynchronous parallel execution. However, adaptation of such schemes to sparse matrices is harder and often impractical. In D3M, computation of each domain\u27s discrete DtN map ``embarrassingly parallel\u27\u27, whereas the customized block LDLT is suitable for a block directed acyclic graph (B-DAG) task scheduling, similar to that used in dense matrix parallel direct solvers. In this approach, computations are represented as a sequence of small tasks that operate on domains of DDM or dense matrix blocks of the reduced matrix. These tasks can be statically scheduled for parallel execution using their DAG dependencies and weights that depend on estimates of computation and communication costs. Comparisons with state-of-the-art exact direct solvers on electrically large problems suggest up to 20% better parallel efficiency, 30% - 3X less memory and slightly faster in runtime, while maintaining the same accuracy

Phasage d’haplotypes par ASP à partir de longues lectures : une approche d’optimisation flexible

Version non corrigée. Une nouvelle version sera disponible d'ici mars 2023.Each chromosome of a di- or polyploid organism has several haplotypes, which are highly similar but diverge on a certain number of positions. However, most of the reference genomes only provide a single sequence for each chromosome, and therefore do not reflect the biological reality.Yet, it is crucial to have access to this information, which is useful in medicine, agronomy and population studies. The recent development of third generation technologies, especially PacBio and Oxford Nanopore Technologies sequencers, has allowed for the production of long reads that facilitate haplotype sequence reconstruction.Bioinformatics methods exist for this task, but they provide only a single solution. This thesis introduces an approach for haplotype phasing based on the search of connected components in a read similarity graph to identify haplotypes. This method uses Answer Set Programming to work on the set ofoptimal solutions. This phasing algorithm has been used to reconstruct haplotypes of the diploid rotifer Adineta vaga.Chaque chromosome d’organisme di- ou polyploïde présente plusieurs haplotypes, qui sont fortement similaires mais divergent sur un certain nombre de positions. Cependant, la majorité des génomes de référence ne renseignent qu’une seule séquence pour chaque chromosome, et ne reflètent donc pas la réalité biologique. Or, il est crucial d’avoir accès à ces informations, qui sont utiles en médecine, en agronomie ou encore dans l’étude des populations. Le récent développement des technologies de troisième génération, notamment des séquenceurs PacBio et Oxford NanoporeTechnologies, a permis la production de lectures longues facilitant la reconstruction des séquences d’haplotypes. Il existe pour cela des méthodes bioinformatiques, mais elles ne fournissent qu’une unique solution. Cette thèse propose une méthode de phasage d’haplotype basée sur la recherchede composantes connexes dans un graph de similarité des lectures pour identifier les haplotypes. Cette méthode utilise l’Answer Set Programming pour travailler sur l’ensemble des solutions optimales. L’algorithme de phasage a permis de reconstruire les haplotypes du rotifère diploïde Adineta vaga