Sparse matrix-matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix-matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM , to choose the right algorithm and data structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.

Multithreaded sparse matrix-matrix multiplication for many-core and GPU architectures

The Jaccard similarity index is an important measure of the overlap of two sets, widely used in machine learning, computational genomics, information retrieval, and many other areas. We design and implement SimilarityAtScale, the first communication-efficient distributed algorithm for computing the Jaccard similarity among pairs of large datasets. Our algorithm provides an efficient encoding of this problem into a multiplication of sparse matrices. Both the encoding and sparse matrix product are performed in a way that minimizes data movement in terms of communication and synchronization costs. We apply our algorithm to obtain similarity among all pairs of a set of large samples of genomes. This task is a key part of modern metagenomics analysis and an evergrowing need due to the increasing availability of high-throughput DNA sequencing data. The resulting scheme is the first to enable accurate Jaccard distance derivations for massive datasets, using large-scale distributed-memory systems. We package our routines in a tool, called GenomeAtScale, that combines the proposed algorithm with tools for processing input sequences. Our evaluation on real data illustrates that one can use GenomeAtScale to effectively employ tens of thousands of processors to reach new frontiers in large-scale genomic and metagenomic analysis. While GenomeAtScale can be used to foster DNA research, the more general underlying SimilarityAtScale algorithm may be used for high-performance distributed similarity computations in other data analytics application domains.

Communication-Efficient Jaccard similarity for High-Performance Distributed Genome Comparisons

The Jaccard similarity index is an important measure of the overlap of two sets, widely used in machine learning, computational genomics, information retrieval, and many other areas. We design and implement SimilarityAtScale, the first communication-efficient distributed algorithm for computing the Jaccard similarity among pairs of large datasets. Our algorithm provides an efficient encoding of this problem into a multiplication of sparse matrices. Both the encoding and sparse matrix product are performed in a way that minimizes data movement in terms of communication and synchronization costs. We apply our algorithm to obtain similarity among all pairs of a set of large samples of genomes. This task is a key part of modern metagenomics analysis and an evergrowing need due to the increasing availability of high-throughput DNA sequencing data. The resulting scheme is the first to enable accurate Jaccard distance derivations for massive datasets, using largescale distributed-memory systems. We package our routines in a tool, called GenomeAtScale, that combines the proposed algorithm with tools for processing input sequences. Our evaluation on real data illustrates that one can use GenomeAtScale to effectively employ tens of thousands of processors to reach new frontiers in large-scale genomic and metagenomic analysis. While GenomeAtScale can be used to foster DNA research, the more general underlying SimilarityAtScale algorithm may be used for high-performance distributed similarity computations in other data analytics application domains.

Communication-Efficient Jaccard Similarity for High-Performance Distributed Genome Comparisons

The Emu Chick is a prototype system designed around the concept of migratory memory-side processing. Rather than transferring large amounts of data across power-hungry, high-latency interconnects, the Emu Chick moves lightweight thread contexts to near-memory cores before the beginning of each memory read. The current prototype hardware uses FPGAs to implement cache-less "Gossamer" cores for doing computational work and a stationary core to run basic operating system functions and migrate threads between nodes. In this initial characterization of the Emu Chick, we study the memory bandwidth characteristics of the system through benchmarks like STREAM, pointer chasing, and sparse matrix vector multiply. We compare the Emu Chick hardware to architectural simulation and Intel Xeon-based platforms. While it is difficult to accurately compare prototype hardware with existing systems, our initial evaluation demonstrates that the Emu Chick uses available memory bandwidth more efficiently than a more traditional, cache-based architecture. Moreover, the Emu Chick provides stable, predictable performance with 80% bandwidth utilization on a random-access pointer chasing benchmark with weak locality.

An Initial Characterization of the Emu Chick

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix-matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and data structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.

Multi-threaded Sparse Matrix-Matrix Multiplication for Many-Core and GPU Architectures

There is growing evidence that current architectures do not well handle cache-unfriendly applications such as sparse math operations, data analytics, and graph algorithms. This is due, in part, to the irregular memory access patterns demonstrated by these applications, and in how remote memory accesses are handled. This paper introduces a new, highly-scalable PGAS memory-centric system architecture where migrating threads travel to the data they access. Scaling both memory capacities and the number of cores can be largely invisible to the programmer.The first implementation of this architecture, implemented with FPGAs, is discussed in detail. A comparison of key parameters with a variety of today's systems, of differing architectures, indicates the potential advantages. Early projections of performance against several well-documented kernels translate these advantages into comparative numbers. Future implementations of this architecture may expand the performance advantages by the application of current state of the art silicon technology.

Highly scalable near memory processing with migrating threads on the emu system architecture

We present an implementation of the Jaccard Index for graphs on the Migratory Memory-Side Processing Emu architecture. This index was designed to find similarities between different vertices in a graph, and is often used to identify communities. The Emu architecture is a parallel system based on a partitioned global address space, with threads automatically migrating inside the memory. We introduce the parallel programming model used to exploit it, detail our implementation of the algorithm, and analyze simulated performance results as well as early hardware tests. We discuss its application to large scale problems.

Implementing the Jaccard Index on the Migratory Memory-Side Processing Emu Architecture

This paper explores a computational deblurring algorithm that will ultimately be implemented in an embedded system with a targeted form factor of 2″×2″×3″. The deblurring algorithm completes a Fourier filtering step followed by a wavelet transform denoising step on a 1080×1920 Bayer input 30 frame per second video feed. A major challenge in performing this processing in real time is that the wavelet denoising process utilizes the stationary wavelet transform, thus exploding the bandwidth requirements of the algorithm. To reach the desired form-factor and performance rate, a hardware accelerator is required. While both GPU and FPGA implementations have been pursued, this paper limits itself to describing our successful implementation using a desktop GPU card. Additionally, we briefly highlight methods, left for future work, for improving GPU performance based on our FPGA implementation efforts that should aid in scaling from our current desktop implementation to an embedded implementation.

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Timothy J. Dysart

Papers

Highly scalable near memory processing with migrating threads on the emu system architecture

Implementing the Jaccard Index on the Migratory Memory-Side Processing Emu Architecture

Embedded real-time HD video deblurring