the router radix is limited to radix-64, the network can scale up to 64k nodes with three dimensions.
However, to scale the network further, the number of dimensions of the flattened butterfly needs
to be increased - which can create packaging difficulties as well as increase cost and latency. In
addition, most of the channels (two of the three dimensions) require global or expensive channels
which significantly increase the cost. To overcome this limitation, a collection of routers can be used
together to create a very high-radix virtual router. The dragonfly topology [ 38 ] described in this
section leverages this concept of a virtual router to create a more scalable topology.
Figure 4.8: (a) High-level block diagram of dragonfly topology and (b) a virtual high-radix router.
The dragonfly is a hierarchical network with three levels: router, group, and system as shown in
Figure 4.8 . At the bottom level, each router has three different type of connections : 1) connections
to p terminals, 2) a −
1 local channels to other routers in the same group, and 3) h global channels
to routers in other groups. Hence, the radix (or degree) of each router is k
group consists of a routers connected via an intra-group interconnection network formed from local
channels. Each group has ap connections to terminals and ah connections to global channels, and
all of the routers in a group collectively act as a virtual router with radix k = a(p + h) . As shown in