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size and 2size. The definition of size depends on the size of the graph to order. Large graphs cannot afford very small values, because the number of blocks becomes much too large and limits the acceleration of BLAS 3 routines, while large values do not help reducing enough the complexity of ILU(k) solving. strat=strat Ordering strategy to be performed. After the ordering strategy is applied, the resulting separators tree is traversed and all of the column blocks that are larger than 2size are split into smaller column blocks, without changing the ordering that has been computed. c Compression method [2]. The parameters of the compression method are listed below. rat=rat Set the compression ratio over which graphs and meshes will not be compressed. Useful values range between 0.7 and 0.8. cpr=strat Ordering strategy to use on the compressed graph or mesh if its size is below the compression ratio times the size of the original graph or mesh. unc=strat Ordering strategy to use on the original graph or mesh if the size of the compressed graph or mesh were above the compression ratio times the size of the original graph or mesh. d Block Halo Approximate Minimum Degree method [49]. The parameters of the Halo Approximate Minimum Degree method are listed below. The Block Halo Approximate Minimum Fill method, described below, is more efficient and should be preferred. cmin=size Minimum number of columns per column block. All column blocks of width smaller than size are amalgamated to their parent column block in the elimination tree, provided that it does not violate the cmax constraint. cmax=size Maximum number of column blocks over which some column block will not amalgamate one of its descendents in the elimination tree. This parameter is mainly designed to provide an upper bound for block size in the context of BLAS3 computations ; else, a huge value should be provided. frat=rat Fill-in ratio over which some column block will not amalgamate one of its descendents in the elimination tree. Typical values range from 0.05 to 0.10. f Block Halo Approximate Minimum Fill method. The parameters of the Halo Approximate Minimum Fill method are listed below. cmin=size Minimum number of columns per column block. All column blocks of width smaller than size are amalgamated to their parent column block in the elimination tree, provided that it does not violate the cmax constraint. 60