Related papers: A Geometric Approach to Matrix Ordering
Partitioning a graph into balanced blocks such that few edges run between blocks is a key problem for large-scale distributed processing. A current trend for partitioning huge graphs are streaming algorithms, which use low computational…
The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…
When applying automatic analysis of fluorescence or histopathological images of cells, it is necessary to partition, or de-clump, partially overlapping cell nuclei. In this work, I describe a method of partitioning partially overlapping…
We present a new method for mapping applications' MPI tasks to cores of a parallel computer such that applications' communication time is reduced. We address the case of sparse node allocation, where the nodes assigned to a job are not…
This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from…
We tackle the problem of graph partitioning for image segmentation using correlation clustering (CC), which we treat as an integer linear program (ILP). We reformulate optimization in the ILP so as to admit efficient optimization via…
We propose a fine-grained hypergraph model for sparse matrix-matrix multiplication (SpGEMM), a key computational kernel in scientific computing and data analysis whose performance is often communication bound. This model correctly describes…
In this paper, an efficient divide-and-conquer (DC) algorithm is proposed for the symmetric tridiagonal matrices based on ScaLAPACK and the hierarchically semiseparable (HSS) matrices. HSS is an important type of rank-structured…
We present a shared-memory parallelization of flow-based refinement, which is considered the most powerful iterative improvement technique for hypergraph partitioning at the moment. Flow-based refinement works on bipartitions, so current…
We present a fast algorithm for linear least squares problems governed by hierarchically block separable (HBS) matrices. Such matrices are generally dense but data-sparse and can describe many important operators including those derived…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
Hypergraph partitioning is a pervasive NP-hard problem, and accelerating its computation on GPU can both slice time-to-solution and raise quality of results. In this work, we implement a multi-level hypergraph partitioning algorithm on GPU…
We present a highly scalable algorithm for multiplying sparse multivariate polynomials represented in a distributed format. This algo- rithm targets not only the shared memory multicore computers, but also computers clusters or specialized…
Modern trends in data collection are bringing current mainstream techniques for database query processing to their limits. Consequently, various novel approaches for efficient query processing are being actively studied. One such approach…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
Scalable sparse LU factorization is critical for efficient numerical simulation of circuits and electrical power grids. In this work, we present a new scalable sparse direct solver called Basker. Basker introduces a new algorithm to…
The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
The increasing importance of multicore processors calls for a reevaluation of established numerical algorithms in view of their ability to profit from this new hardware concept. In order to optimize the existent algorithms, a detailed…