Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout

TL;DR

This paper presents a task-parallel incomplete Cholesky factorization algorithm using a 2D block layout, enabling efficient execution on manycore architectures with significant speedups demonstrated on Intel Xeon Phi.

Contribution

The paper introduces a novel task-parallel algorithm with a 2D block layout and a portable API for manycore platforms, improving performance over traditional methods.

Findings

Achieved 26.6x speedup over single-threaded implementation.

Demonstrated 19.2x speedup over serial Cholesky without tasking overhead.

Validated performance on Intel Sandybridge and Xeon Phi platforms.

Abstract

We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block layout. The algorithm-by-blocks approach induces a task graph for the factorization. These tasks are inter-related to each other through their data dependences in the factorization algorithm. To process the tasks on various manycore architectures in a portable manner, we also present a portable tasking API that incorporates different tasking backends and device-specific features using an open-source framework for manycore platforms i.e., Kokkos. A performance evaluation is presented on both Intel Sandybridge and Xeon Phi platforms for matrices from the University of Florida sparse matrix collection to illustrate merits of the proposed task-based factorization. Experimental results demonstrate that our task-parallel implementation delivers about 26.6x speedup (geometric mean) over single-threaded incomplete Cholesky-by-blocks and 19.2x speedup over serial Cholesky performance which does not carry tasking overhead using 56 threads on the Intel Xeon Phi processor for sparse matrices arising from various application problems.