Title: A High-Throughput Solver for Marginalized Graph Kernels on GPU

Abstract

Here, we present the design and optimization of a solver for efficient and high-throughput computation of the marginalized graph kernel on General Purpose GPUs. The graph kernel is computed using the conjugate gradient method to solve a generalized Laplacian of the tensor product between a pair of graphs. To cope with the large gap between the instruction throughput and the memory bandwidth of the GPUs, our solver forms the graph tensor product on-the-fly without storing it in memory. This is achieved by using threads in a warp cooperatively to stream the adjacency and edge label matrices of individual graphs by small square matrix blocks called tiles, which are then staged in registers and the shared memory for later reuse. Warps across a thread block can further share tiles via the shared memory to increase data reuse. We exploit the sparsity of the graphs hierarchically by storing only non-empty tiles using a coordinate format and nonzero elements within each tile using bitmaps. We propose a new partition-based reordering algorithm for aggregating nonzero elements of the graphs into fewer but denser tiles to further exploit sparsity. We carry out extensive theoretical analyses on the graph tensor product primitives for tiles of variousmore » density and evaluate their performance on synthetic and real-world datasets. Our solver delivers three to four orders of magnitude speedup over existing CPU-based solvers such as GraKeL and GraphKernels. The capability of the solver enables kernel-based learning tasks at unprecedented scales.« less

Authors:

Tang, Yu-Hang ^[1]; Selvitopi, Oguz ^[1]; Popovici, Doru Thom ^[1]; Buluc, Aydin ^[1]

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+ Show Author Affiliations

1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Publication Date:

Fri May 01 00:00:00 EDT 2020

Research Org.:

Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:

1582329

Grant/Contract Number:  

AC02-05CH11231; AC05-00OR22725

Resource Type:

Accepted Manuscript

Journal Name:

2020 IEEE International Parallel and Distributed Processing Symposium (IPDPS)

Additional Journal Information:

Journal Name: 2020 IEEE International Parallel and Distributed Processing Symposium (IPDPS); Journal Volume: 2020; Related Information: see also on arXiv abs/1910.06310

Publisher:

IEEE

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; kernel; symmetric matrices; linear systems; mathematical model; tensile stress; task analysis; graphics processing units