Multilevel Algorithms for Wavefront Reduction

Multilevel algorithms are proposed for reordering sparse symmetric matrices to reduce the wavefront and proole. A graph representation of the matrix is used and two graph coarsening methods are investigated. A multilevel algorithm that uses a maximal independent vertex set for coarsening and the Sloan algorithm on the coarsest graph is shown to produce orderings that are of a similar quality to those obtained using the best existing combinatorial algorithm (the hybrid Sloan algorithm). Advantages of the proposed algorithm over the the hybrid Sloan algorithm are that it does not require any spectral information and is signiicantly faster, requiring on average half the CPU time.