Simulated Annealing for Profile and Fill Reduction of Sparse Matrices

Simulated annealing can minimize both profile and fill of sparse matrices. We applied these techniques to a number of sparse matrices from the Harwell-Boeing Sparse Matrix Collection. We were able to reduce profile typically to about 80% of that attained by conventional profile minimization techniques (and sometimes much lower), but fill reduction was less successful (85% at best). We present a new algorithm that significantly speeds up profile computation during the annealing process. Simulated annealing is, however, still much more time-consuming than conventional techniques and is therefore likely to be useful only in situations where the same sparse matrix is being used repeatedly.