Parallel Implementations of RCM Algorithm for Bandwidth Reduction of Sparse Matrices

The Reverse Cuthill-McKee (RCM) algorithm is a well-known heuristicfor reordering sparse matrices. It is typically used to speed up the computation ofsparse linear systems of equations. This paper describes two parallel approachesfor the RCM algorithm as well as an optimized version of each one based on someproposed enhancements. The first one exploits a strategy for reducing lazy threads,while the second one makes use of a static bucket array as the main data structureand suppress some steps performed by the original algorithm. These related changesled to outstanding reordering time results and significant bandwidth reductions.The performance of two algorithms is compared with the respective implementationmade available by Boost library. The OpenMP framework is used for supportingthe parallelism and both versions of the algorithm are tested with large sparse andstructural symmetric matrices.