Simulated annealing for profile and fill reduction of sparse matrices

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Abstract
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 per cent of that attained by conventional profile minimization techniques (and sometimes much lower), but fill reduction was less successful (85 per cent 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.

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