This paper describes the equation ordering algorithms implemented in ASReml 2 (http://www.asreml.co.uk) and directly compares them with the publicly available MeTiS routines (http://www-users.cs.umn.edu/\textasciitildekarypis/metis/metis/download.html). Meyer (2005) found the MeTis routines halved the execution time in her software when compared with minimum degree algorithms. We provide evidence that the algorithm in ASReml 2 is generally better than the MeTiS routines when used in ASReml. Although the MeTiS routines are usually faster at determining an order, the ASReml algorithm generally produces a smaller inverse resulting in a 20% faster execution time per iteration on average. ASReml performs a symbolic absorption of the mixed model equations, always choosing to absorb one of the rows with the fewest non-zero elements. The order is not unique and rearranging the initial order of equations will result in a different processing order.

A. R Gilmour, R. Thompson

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume , , 27.13, 2006
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