A High-Throughput Solver for Marginalized Graph Kernels on GPU

TL;DR

This paper introduces a GPU-based high-throughput solver for marginalized graph kernels, significantly accelerating kernel evaluations for large graph datasets using innovative on-the-fly tensor product computation and optimized memory reuse.

Contribution

The paper presents a novel GPU solver that efficiently computes marginalized graph kernels by on-the-fly tensor product formation and hierarchical sparsity exploitation, achieving 1000x speedup over CPU methods.

Findings

Achieves 3-4 orders of magnitude speedup over CPU solvers.

Enables kernel-based learning on large-scale graph datasets.

Demonstrates effectiveness on synthetic and real-world graphs.

Abstract

We present the design and optimization of a linear solver on General Purpose GPUs for the efficient and high-throughput evaluation of the marginalized graph kernel between pairs of labeled graphs. The solver implements a preconditioned conjugate gradient (PCG) method to compute the solution to a generalized Laplacian equation associated with the tensor product of two graphs. To cope with the gap between the instruction throughput and the memory bandwidth of current generation GPUs, our solver forms the tensor product linear system on-the-fly without storing it in memory when performing matrix-vector dot product operations in PCG. Such on-the-fly computation is accomplished by using threads in a warp to cooperatively 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. Besides, we propose a new partition-based reordering algorithm for aggregating nonzero elements of the graphs into fewer but denser tiles to improve the efficiency of the sparse format. We carry out extensive theoretical analyses on the graph tensor product primitives for tiles of various 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.