Related papers: Massively Parallel Reductions in Multivariate Poly…
Subgraph isomorphism is a well-known NP-hard problem that is widely used in many applications, such as social network analysis and query over the knowledge graph. Due to the inherent hardness, its performance is often a bottleneck in…
In this work, we present an extension of Gaussian process (GP) models with sophisticated parallelization and GPU acceleration. The parallelization scheme arises naturally from the modular computational structure w.r.t. datapoints in the…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in…
We present a recursive way to partition hypergraphs which creates and exploits hypergraph geometry and is suitable for many-core parallel architectures. Such partitionings are then used to bring sparse matrices in a recursive Bordered Block…
Recent implementations of local approximate Gaussian process models have pushed computational boundaries for non-linear, non-parametric prediction problems, particularly when deployed as emulators for computer experiments. Their flavor of…
Purpose: Design of a preconditioner for fast and efficient parallel imaging and compressed sensing reconstructions. Theory: Parallel imaging and compressed sensing reconstructions become time consuming when the problem size or the number of…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
Processors with large numbers of cores are becoming commonplace. In order to take advantage of the available resources in these systems, the programming paradigm has to move towards increased parallelism. However, increasing the level of…
The high-energy physics community is investigating the potential of deploying machine-learning-based solutions on Field-Programmable Gate Arrays (FPGAs) to enhance physics sensitivity while still meeting data processing time constraints. In…
Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…
We discuss an approach for solving sparse or dense banded linear systems ${\bf A} {\bf x} = {\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\bf A} \in {\mathbb{R}}^{N \times N}$ is possibly nonsymmetric and moderately large;…
We present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With…
This paper introduces a strategy for signature-based algorithms to compute Groebner basis. The signature-based algorithms generate S-pairs instead of S-polynomials, and use s-reduction instead of the usual reduction used in the Buchberger…
Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…
The signatures of polynomials were originally introduced by Faug\`{e}re for the efficient computation of Gr\"obner bases [Fau02], and redefined by Arri-Perry [AP11] as the standard monomials modulo the module of syzygies. Since it is…
Gaussian Process Regression (GPR) is an important type of supervised machine learning model with inherent uncertainty measure in its predictions. We propose a new framework, nuGPR, to address the well-known challenge of high computation…
Recent work showed that compiling functional programs to use dense, serialized memory representations for recursive algebraic datatypes can yield significant constant-factor speedups for sequential programs. But serializing data in a…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
A great variety of fundamental optimization and counting problems arising in computer science, mathematics and physics can be reduced to one of the following computational tasks involving polynomials and set systems: given an $m$-variate…