Difference between All-to-All Reduction and All-Reduce in MPI

Question

Trying to figure out the difference between All-to-All Reduction and All-Reduce in open MPI. From my understanding All-to-One Reduction takes a piece m (integer, array, etc..) from all processes and combines all the pieces together with an operator (min, max, sum, etc..) and stores it in the selected process. From this i assume that All-to-All Reduction is the same but the product is stored in all the processes instead of just one. From this document it seems like All-Reduce is basically doing the same as All-to-All Reduction, is this right or am i getting it wrong?

Answer 1

The all-reduce (MPI_Allreduce) is a combined reduction and broadcast (MPI_Reduce, MPI_Bcast). They might have called it MPI_Reduce_Bcast. It is important to note that a MPI reduction does not do any global reduction. So if have 10 numbers each on 5 processes, after a MPI_Reduce one process has 10 numbers. After MPI_Allreduce, all 5 processes have the same 10 numbers.

In contrast, the all-to-all reduction performs a reduction and scatter, hence it is called MPI_Reduce_scatter[_block]. So if you have 10 numbers each on 5 processes, after a MPI_Reduce_scatter_block, the 5 processes have 2 numbers each. Note that MPI doesn't itself use the terminology all-to-all reduction, probably due to the misleading ambiguity.