What Is a Virtual Topology?

Topology is an extra, optional attribute you can give to a communicator. The assigned topology can correspond to the network interconnect between processes or some other aspect of the underlying hardware, but it does not have to.

• Simple linear rank (0,1,... n-1) may not adequately express the communication pattern.
• Often, communication between processes is logically arranged in a pattern such as a 2- or 3-dimensional grid.
• This logical process arrangement is generally described by a graph or “virtual topology”.

How to Use Virtual Topologies

• Creating a topology produces a new communicator.
• MPI provides mapping functions; between old and new communicators.
• Mapping functions compute processor ranks in a manner consistent with the specified topology.

Topology Types

Cartesian topologies

• Each process is connected to its neighbors in a virtual n-dimensional grid.
• Boundaries in each dimension can be cyclic (periodic), or not.
• Result: processes can be conveniently identified by Cartesian coordinates.

Graph topologies (not covered in this topic)

• Graphs (undirected graphs)
• Distributed graphs (directed graphs; noncollective)

Neighborhood collectives

• Defined over existing topologies
• Allows programmer to induce a communicator for neighboring nodes