Collective communication of receiver-selective data using MPI Allgather, MPI Alltoall, and MPI Alltoallv. The three panels illustrate send and receive buffers for the example of an MPI communication that involves three ranks. Homogeneous data types are required throughout the entire send and receive buffer. Squares represent single buffer entries. Data sent by rank 0, rank 1, and rank 2 are shown in dark gray, light gray, and medium gray, respectively. To indicate receiver selectivity, we define the data marked with “x” to be required on rank 1 and rank 2 but not on rank 0. (A) MPI Allgather: All ranks receive the entire send buffer from all ranks, which can include irrelevant data, for example, the receive buffer on rank 0 contains an “x”-entry with data that is not required. The receive buffer is a concatenation of all send buffers and the receive buffer size hence scales with the total number of ranks taking part in the communication (assuming fixed send buffer sizes). Send buffers of equal size and hence also receive buffers of equal size are required for all ranks, which can entail sending empty buffer entries (unfilled squares). (B) MPI Alltoall: Send buffers consist of equally sized sections that are destined for different receiving ranks. This allows each rank to define the data to be transmitted to any particular rank. Each rank has to send identically-sized buffer sections to each rank, which can entail sending empty buffer entries or even entirely empty buffer sections. Rank 2, for example, sends an empty buffer section to rank 1. The size of the receive buffers is identical to the size of the send buffers and independent of the number of ranks participating in the communication. To send specific data to multiple ranks, the sending rank needs to copy the data to the send-buffer sections of all intended receiving ranks, which leads to redundancy in the send buffer; rank 0, for example, sends an “x”-entry to both, rank 1 and 2. (C) MPI Alltoallv: Similar to MPI Alltoall, send buffers consist of sections that are destined for different receiving ranks. However, the sections are allowed to differ in size avoiding empty buffer entries. Adapted from Jordan et al. (2018) under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/).