Irregular Personalized Communication on Distributed Memory Machines

In this paper we present several algorithms for performing all-to-many personalized communication on distributed memory parallel machines. We assume that each processor sends a di erent message (of potentially di erent size) to a subset of all the processors involved in the collective communication. The algorithms are based on decomposing the communication matrix into a set of partial permutations. We study the e ectiveness of our algorithms both from the view of static scheduling and from runtime scheduling.