Johnsson, S. LennartHo, Ching-Tien2016-03-031991Johnsson, S. Lennart and Ching-Tien Ho. 1991. Optimal All-to-All Personalized Communication with Minimum Span on Boolean Cubes. Harvard Computer Science Group Technical Report TR-18-91.http://nrs.harvard.edu/urn-3:HUL.InstRepos:25680330All-to-all personalized communication is a class of permutations in which each processor sends a unique message to every other processor. We present optimal algorithms for concurrent communication on all channels in Boolean cube networks, both for the case with a single permutation, and the case where multiple permutations shall be performed on the same local data set, but on different sets of processors. For K elements per processor our algorithms give the optimal number of elements transfer, K=2. For a succession of all-to-all personalized communications on disjoint subcubes of β dimensions each, our best algorithm yields (K/2)+σ-β element exchanges in sequence, where is the total number of processor dimensions in the permutation. An implementation on the Connection Machine of one of the algorithms offers a maximum speed-up of 50% compared to the previously best known algorithm.en-USResearch Paper or Report2016-03-03