Topology

1
Topology

• A single shared bus is not necessarily the best
  way to connect processors/memory
• Vulnerable to saturation
• Topological measures
• Diameter
• The greatest distance between any two nodes
• Node degree/valance
• The number of edges joining it to other nodes

2
Fully Connected Network

• The most powerful interconnection network
  topology
• Each node is directly connected to ALL other
  nodes
• Advantages
• Low diameter (always 1)
• Disadvantage
• Does not scale well
• Large number of links
• N(N-1) / 2

3
Rings

• A simple ring is just a linear array with the end
  nodes linked.
• Advantage
• Low degree (always 2)
• Disadvantage
• Diameter grows proportionately to the number of
  nodes

4
Mesh and Torus

• In a mesh, processors are laid out along the axis
  of a D-dimensional grid
• A Torus is a mesh whose edges wrap around
• These topologies are popular
• They are simple to construct
• Their diameter grows as Sqrt( P )
• Can be expanded easily
• Many matrix calculations fit this topology

5
Mesh and Torus
6
Hypercube
7
Hypercube

• Advantages
• Perfect routing is easy to implement
• Diameter grows logarithmically with the number of
  processors
• Many topologies can be embedded in hypercubes
• Hypercubes have lots of links