The Reverse Cuthill-McKee Algorithm in Distributed-Memory

TL;DR

This paper introduces the first distributed-memory implementation of the reverse Cuthill-McKee algorithm, enabling efficient sparse matrix reordering at scale for high-performance computing applications.

Contribution

It presents a novel distributed-memory parallelization of RCM using 2D matrix decomposition, achieving high scalability and performance.

Findings

Strong scaling up to 1024 cores for small matrices

Scaling up to 4096 cores for large matrices

Efficient primitive-based implementation

Abstract

Ordering vertices of a graph is key to minimize fill-in and data structure size in sparse direct solvers, maximize locality in iterative solvers, and improve performance in graph algorithms. Except for naturally parallelizable ordering methods such as nested dissection, many important ordering methods have not been efficiently mapped to distributed-memory architectures. In this paper, we present the first-ever distributed-memory implementation of the reverse Cuthill-McKee (RCM) algorithm for reducing the profile of a sparse matrix. Our parallelization uses a two-dimensional sparse matrix decomposition. We achieve high performance by decomposing the problem into a small number of primitives and utilizing optimized implementations of these primitives. Our implementation shows strong scaling up to 1024 cores for smaller matrices and up to 4096 cores for larger matrices.