On Complexity of Collective Communications on a Fat Cube Topology

A recent renewed interest in hypercube interconnection network has been concentrated to the more scalable version known as a fat cube. The paper introduces several router models for fat nodes and uses them for cost comparison of both the hypercube and fat cube topologies. Analysis of time complexity of collective communications is done next and lower bounds on the number of communication steps are derived. Examples of particular communication algorithms on the 2D-fat cube topology with 8 processors are summarized and described in detail. The performed study shows that a large variety of fat cubes can provide much desired flexibility, trading cost for performance and manufacturability