Number Of Memory Transfers Research Articles

SpEpistasis: A sparse approach for three-way epistasis detection

Epistasis detection is a fundamental application in the areas of bioinformatics and biomedicine, providing important insights regarding the relationship between the human genome and the occurrence of certain diseases. Exhaustive epistasis detection approaches are employed to achieve an accurate and deterministic solution, at the cost of high computational complexity, especially when targeting high-order epistasis. While recent works employ vectorization and cache-blocking techniques to alleviate this burden, these solutions are now limited by the maximum performance of the functional units of computing systems. Thus, to further improve the performance of epistasis detection it is necessary to reduce its number of memory transfers and computations. To tackle this issue, this work proposes SpEpistasis, which performs three-way epistasis detection by relying on sparse features, which by only storing the non-zero elements of the dataset, allows for reducing the number of operations needed for epistasis detection. To achieve this goal, a new hybrid format to represent the input dataset is proposed, which stores a subset of the data in the compressed sparse row format. Moreover, new sparse-aware algorithmic approaches are also proposed in order to leverage both the hybrid format and the vector capabilities of current CPUs from Intel, AMD, and ARM. The experimental results show that SpEpistasis provides a speedup up to 3.7× and average speedups of around 1.8× and 1.33× when compared with other state-of-the-art works.

Hybrid Direct and Iterative Solver with Library of Multi-criteria Optimal Orderings for h Adaptive Finite Element Method Computations

In this paper we present a multi-criteria optimization of element partition trees and resulting orderings for multi-frontal solver algorithms executed for two dimensional h adaptive finite element method. In particular, the problem of optimal ordering of elimination of rows in the sparse matrices resulting from adaptive finite element method computations is reduced to the problem of finding of optimal element partition trees. Given a two dimensional h refined mesh, we find all optimal element partition trees by using the dynamic programming approach. An element partition tree defines a prescribed order of elimination of degrees of freedom over the mesh. We utilize three different metrics to estimate the quality of the element partition tree. As the first criterion we consider the number of floating point operations(FLOPs) performed by the multi-frontal solver.As the second criterion we consider the number of memory transfers (MEMOPS) performed by the multi-frontal solver algorithm. As the third criterion we consider memory usage (NONZEROS) of the multi-frontal direct solver. We show the optimization results for FLOPs vs MEMOPS as well as for the execution time estimated as FLOPs+100*MEMOPS vs NONZEROS. We obtain Pareto fronts with multiple optimal trees, for each mesh, and for each refinement level. We generate a library of optimal elimination trees for small grids with local singularities. We also propose an algorithm that for a given large mesh with identified local sub-grids, each one with local singularity. We compute Schur complements over the sub-grids using the optimal trees from the library, and we submit the sequence of Schur complements into the iterative solver ILUPCG.