Interconnection Networks
1. Topologies
 View switched network as a graph
 Vertices = processors or switches
 Edges = communication paths
 Two kinds of topologies
 Direct
 Indirect
2. Direct topology
 Ratio of switch nodes to processor nodes is 1:1
 Every switch node is connected to
 1 processor node
 At least 1 other switch node
3. Indirect topology
 Ratio of switch nodes to processor nodes is greater than 1:1
 Some switches simply connect other switches
4. Measures to evaluate the interconnection networks
 Diameter
 distance between farthest two nodes
 Clique K_n best: d = O(1)
 but #edges m = O(n^2);
 m = O(n) in a path P_n or cycle C_n, but d = O(n) as well
 Bisection width
 Min. number of edges in a cut which roughly divides a network in two halves determines the min. bandwidth of the network
 K_n’s bisection width is O(n), but C_n’s O(1)
 Degree = Number of edges / node
 constant degree board can be mass produced
 Constant edge length? (yes/no)
 Planar? – easier to build
5. 2-D Mesh Network and Evaluation
 Direct topology
 Switches arranged into a 2-D lattice
 Communication allowed only between neighboring switches
 Variants allow wraparound connections between switches on edge of mesh
 Diameter: (n1/2)
 m = (n)
 Bisection width: (n1/2)
 Number of edges per switch: 4
 Constant edge length? Yes
 planar
6. Hypercube Network and Evaluation
 Direct Topology
 2 x 2 x … x 2 mesh
 Number of nodes a power of 2
 Node addresses 0, 1, …, 2k-1
 Node i connected to k nodes whose addresses differ from i in exactly one bit position
 Diameter: log n
 Bisection width: n / 2
 Edges per node: log n
 Constant edge length? No
4. Binary Tree Network and Evaluation
 Indirect topology
 n = 2d processor nodes, n-1 switches
 Diameter: 2 log n
 M = O(n)
 Bisection width: 1
 Edges / node: 3
 Constant edge length? No
 planar
7. Omega Network and Evaluation
 Indirect topology
 Number of nodes a power of 2
 Nodes have addresses 0, 1, …, 2k-1
 Diameter: log n
 Bisection width: n / 2
 Edges per node: 4
 Constant edge length? No