Multicore Max-Flow using GraphBLAS: A Usability Study

Optimizing linear algebra operations has been a research topic for decades. The compact language of mathematics also produce lean, maintainable code. Using linear algebra as a high-level abstraction for graph operations is therefore very attractive. In this work, we will explore the usability of the GraphBLAS framework, currently the leading standard for graph operations that uses linear algebra as an abstraction. We analyze the usability of GraphBLAS by using it to implement the Edmonds-Karp algorithm for s-t maximum-flow/minimum-cut. To our knowledge, this work represents the first published results of Max-Flow in GraphBLAS. The result of our novel implementation was an algorithm that achieved a speedup of up to 11 over its own baseline, and is surprisingly compact and easy to reason about

JGraphT -- A Java library for graph data structures and algorithms

Mathematical software and graph-theoretical algorithmic packages to efficiently model, analyze and query graphs are crucial in an era where large-scale spatial, societal and economic network data are abundantly available. One such package is JGraphT, a programming library which contains very efficient and generic graph data-structures along with a large collection of state-of-the-art algorithms. The library is written in Java with stability, interoperability and performance in mind. A distinctive feature of this library is the ability to model vertices and edges as arbitrary objects, thereby permitting natural representations of many common networks including transportation, social and biological networks. Besides classic graph algorithms such as shortest-paths and spanning-tree algorithms, the library contains numerous advanced algorithms: graph and subgraph isomorphism; matching and flow problems; approximation algorithms for NP-hard problems such as independent set and TSP; and several more exotic algorithms such as Berge graph detection. Due to its versatility and generic design, JGraphT is currently used in large-scale commercial, non-commercial and academic research projects. In this work we describe in detail the design and underlying structure of the library, and discuss its most important features and algorithms. A computational study is conducted to evaluate the performance of JGraphT versus a number of similar libraries. Experiments on a large number of graphs over a variety of popular algorithms show that JGraphT is highly competitive with other established libraries such as NetworkX or the BGL.Comment: Major Revisio

Large Scale Enrichment and Statistical Cyber Characterization of Network Traffic

Modern network sensors continuously produce enormous quantities of raw data that are beyond the capacity of human analysts. Cross-correlation of network sensors increases this challenge by enriching every network event with additional metadata. These large volumes of enriched network data present opportunities to statistically characterize network traffic and quickly answer a key question: "What are the primary cyber characteristics of my network data?" The Python GraphBLAS and PyD4M analysis frameworks enable anonymized statistical analysis to be performed quickly and efficiently on very large network data sets. This approach is tested using billions of anonymized network data samples from the largest Internet observatory (CAIDA Telescope) and tens of millions of anonymized records from the largest commercially available background enrichment capability (GreyNoise). The analysis confirms that most of the enriched variables follow expected heavy-tail distributions and that a large fraction of the network traffic is due to a small number of cyber activities. This information can simplify the cyber analysts' task by enabling prioritization of cyber activities based on statistical prevalence.Comment: 8 pages, 8 figures, HPE

Compiler Support for Sparse Tensor Computations in MLIR

Sparse tensors arise in problems in science, engineering, machine learning, and data analytics. Programs that operate on such tensors can exploit sparsity to reduce storage requirements and computational time. Developing and maintaining sparse software by hand, however, is a complex and error-prone task. Therefore, we propose treating sparsity as a property of tensors, not a tedious implementation task, and letting a sparse compiler generate sparse code automatically from a sparsity-agnostic definition of the computation. This paper discusses integrating this idea into MLIR

Efficient Tiled Sparse Matrix Multiplication through Matrix Signatures

International audienceTiling is a key technique to reduce data movement in matrix computations. While tiling is well understood and widely used for dense matrix/tensor computations, effective tiling of sparse matrix computations remains a challenging problem. This paper proposes a novel method to efficiently summarize the impact of the sparsity structure of a matrix on achievable data reuse as a one-dimensional signature, which is then used to build an analytical cost model for tile size optimization for sparse matrix computations. The proposed model-driven approach to sparse tiling is evaluated on two key sparse matrix kernels: Sparse Matrix-Dense Matrix Multiplication (SpMM) and Sampled Dense-Dense Matrix Multiplication (SDDMM). Experimental results demonstrate that model-based tiled SpMM and SDDMM achieve high performance relative to the current state-of-the-art

Algebraic, Block and Multiplicative Preconditioners based on Fast Tridiagonal Solves on GPUs

This thesis contributes to the field of sparse linear algebra, graph applications, and preconditioners for Krylov iterative solvers of sparse linear equation systems, by providing a (block) tridiagonal solver library, a generalized sparse matrix-vector implementation, a linear forest extraction, and a multiplicative preconditioner based on tridiagonal solves. The tridiagonal library, which supports (scaled) partial pivoting, outperforms cuSPARSE's tridiagonal solver by factor five while completely utilizing the available GPU memory bandwidth. For the performance optimized solving of multiple right-hand sides, the explicit factorization of the tridiagonal matrix can be computed. The extraction of a weighted linear forest (union of disjoint paths) from a general graph is used to build algebraic (block) tridiagonal preconditioners and deploys the generalized sparse-matrix vector implementation of this thesis for preconditioner construction. During linear forest extraction, a new parallel bidirectional scan pattern, which can operate on double-linked list structures, identifies the path ID and the position of a vertex. The algebraic preconditioner construction is also used to build more advanced preconditioners, which contain multiple tridiagonal factors, based on generalized ILU factorizations. Additionally, other preconditioners based on tridiagonal factors are presented and evaluated in comparison to ILU and ILU incomplete sparse approximate inverse preconditioners (ILU-ISAI) for the solution of large sparse linear equation systems from the Sparse Matrix Collection. For all presented problems of this thesis, an efficient parallel algorithm and its CUDA implementation for single GPU systems is provided