The evolution of the minimum degree ordering algorithm
Over the past fifteen years, the implementation of the minimum degree algorithm has received much study, and many important enhancements have been made to it. In this article, we describe these various enhancements, trace their historical development, and provide some experiments showing how very effective they are in improving the execution time of the algorithm. We also present a shortcoming that exists in all of the widely used implementations of the algorithm, namely, that the quality of the ordering provided by the implementations is surprisingly sensitive to the initial ordering. For example, changing the input ordering can lead to an increase (or decrease) of as much as a factor of three in the cost of the subsequent numerical factorization. This sensitivity is caused by the lack of an effective tie-breaking strategy, and our experiments illustrate the importance of developing such a strategy.
- Research Organization:
- Oak Ridge National Lab., TN (United States)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 5686483
- Report Number(s):
- ORNL/TM-10452; ON: DE87011705
- Country of Publication:
- United States
- Language:
- ENGLISH
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