Related papers: Communication-Optimal Parallel Standard and Karats…
We propose COSMA: a parallel matrix-matrix multiplication algorithm that is near communication-optimal for all combinations of matrix dimensions, processor counts, and memory sizes. The key idea behind COSMA is to derive an optimal (up to a…
We present a novel, highly efficient algorithm to parallelize O(N^2) direct summation method for N-body problems with individual timesteps on distributed-memory parallel machines such as Beowulf clusters. Previously known algorithms, in…
Mass spectrometry (MS) based omics data analysis require significant time and resources. To date, few parallel algorithms have been proposed for deducing peptides from mass spectrometry-based data. However, these parallel algorithms were…
We improve the space complexity of Karatsuba multiplication on a quantum computer from $O(n^{1.427})$ to $O(n)$ while maintaining $O(n^{\lg 3})$ gate complexity. We achieve this by ensuring recursive calls can add their outputs directly…
Almost asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity $IO_\mathcal{A}\left(n,M\right)$ of a general class of hybrid algorithms computing the product of two integers, each represented with $n$ digits in a…
We give lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast…
Numerical algorithms have two kinds of costs: arithmetic and communication, by which we mean either moving data between levels of a memory hierarchy (in the sequential case) or over a network connecting processors (in the parallel case).…
A parallel algorithm has perfect strong scaling if its running time on P processors is linear in 1/P, including all communication costs. Distributed-memory parallel algorithms for matrix multiplication with perfect strong scaling have only…
In this paper we describe, implement, and test the performance of distributed memory simulations of quantum circuits on the MSU Laconia Top500 supercomputer. Using OpenMP and MPI hybrid parallelization, we first use a distributed…
Processing-in-Memory (PIM) enhances memory with computational capabilities, potentially solving energy and latency issues associated with data transfer between memory and processors. However, managing concurrent computation and data flow…
The communication cost of algorithms (also known as I/O-complexity) is shown to be closely related to the expansion properties of the corresponding computation graphs. We demonstrate this on Strassen's and other fast matrix multiplication…
Parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes…
This thesis develops signal-processing algorithms and implementation schemes under constraints of minimal parallelism and memory space, with the goal of improving energy efficiency of low-power computing hardware. We propose (i) a…
A common approach for designing scalable algorithms for massive data sets is to distribute the computation across, say $k$, machines and process the data using limited communication between them. A particularly appealing framework here is…
We study the scalability of consensus-based distributed optimization algorithms by considering two questions: How many processors should we use for a given problem, and how often should they communicate when communication is not free?…
Bootstrapping is a powerful statistical resampling technique for estimating the sampling distribution of an estimator. However, its computational cost becomes prohibitive for large datasets or a high number of resamples. This paper presents…
Integer arithmetic is the underpinning of many quantum algorithms, with applications ranging from Shor's algorithm over HHL for matrix inversion to Hamiltonian simulation algorithms. A basic objective is to keep the required resources to…
In the research area of parallel computation, the communication cost has been extensively studied, while the IO cost has been neglected. For big data computation, the assumption that the data fits in main memory no longer holds, and…
A new class of parallel algorithms is introduced that can achieve a complexity of O(n^3/2) with respect to the interprocessor communication, in the exact computation of systems with pairwise mutual interactions of all elements. Hitherto,…
We present a new parallel model of computation suitable for spatial architectures, for which the energy used for communication heavily depends on the distance of the communicating processors. In our model, processors have locations on a…