TYPES OF NETWORKS
Topologies can be broken down into two different genres: direct and indirect [ 20 ]. A direct network
has processing nodes attached directly to the switching fabric; that is, the switching fabric is dis-
tributed among the processing nodes. An indirect network has the endpoint network independent
of the endpoints themselves - i.e., dedicated switch nodes exist and packets are forwarded indirectly
through these switch nodes. The type of network determines some of the packaging and cabling
requirements as well as fault resilience. It also impacts cost, for example, since a direct network can
combine the switching fabric and the network interface controller (NIC) functionality in the same
silicon package. An indirect network typically has two separate chips, with one for the NIC and
another for the switching fabric of the network. Examples of direct network include mesh, torus, and
hypercubes discussed in this chapter as well as high-radix topologies such as the flattened butterfly
described in the next chapter. Indirect networks include conventional butterfly topology and fat-tree
The term radix and dimension are often used to describe both types of networks but have been
used differently for each network. For an indirect network, radix often refers to the number of ports
of a switch, and the dimension is related to the number of stages in the network. However, for a
direct network, the two terminologies are reversed - radix refers to the number of nodes within a
dimension, and the network size can be further increased by adding multiple dimensions . The two
terms are actually a duality of each other for the different networks - for example, in order to reduce
the network diameter, the radix of an indirect network or the dimension of a direct network can be
increased. To be consistent with existing literature, we will use the term radix to refer to different
aspects of a direct and an indirect network.
MESH, TORUS, AND HYPERCUBES
The mesh , torus and hypercube networks all belong to the same family of direct networks often referred
to as k -ary n -mesh or k -ary n -cube. The scalability of the network is largely determined by the radix,
k , and number of dimensions, n , with N
k n total endpoints in the network. In practice, the radix of
the network is not necessarily the same for every dimension (Figure 3.2 ). Therefore, a more general
way to express the total number of endpoints is given by Equation 3.1 .
n − 1
i = 0
(a) 8-ary 1-mesh.
(b) 8-ary 1-cube.
Figure 3.1: Mesh (a) and torus (b) networks.