A pseudoperipheral vertex finder based on the George-Liu and Kaveh's B algorithms for small symmetric matrices

This work considers the well-known Reverse Cuthill--McKee method for sparse matrix/graph bandwidth reduction. This method needs a starting vertex. There are many algorithms for generating it, and one of the best-known is the George--Liu algorithm. This paper reports a computational experiment that compares eight pseudoperipheral vertex finders along with a modified method that is a hybrid of the George--Liu and Kaveh's B algorithms. Our simulations then use the resulting vertices as starting points for the Reverse Cuthill--McKee method for bandwidth reduction of sparse matrices. This paper empirically evaluates nine algorithms over a collection of 50 small symmetric matrix instances. This paper shows numerical evidence for the better performance of this variant compared with eight other algorithms for finding a starting vertex for the Reverse Cuthill--McKee method for bandwidth optimization of small matrices with symmetric sparsity patterns at a higher cost than the George--Liu algorithm.