1. Interconnection Networks Communications Among Processors

2. Issues for Networks Total Bandwidth amount of data which can be moved from somewhere to somewhere per unit time Link Bandwidth amount of data which can be moved along one link per unit time Message Latency time from start of sending a message until it is received Bisection Bandwidth amount of data which can move from one half of network to the other per unit time for worst case split of network

3. Issues for Networks Number of connections per node degree of network Number of links as a function of the number of nodes must be linear for a scalable network Diameter maximum of the shortest distance between each pair of nodes

4. Point-to-Point Networks Bus Pipeline, Ring 2-D or 3-D Mesh, Toriodal Mesh Complete Connection Hypercube Cube-connected cycle Binary Tree Fat Tree

5. Ring Topology Number of Links as function of number of nodes, N : N (linear) Number of connections per node: 2 (constant) Link bandwidth = speed of single link, b Total bandwidth = N * b Bisection bandwidth = 2 * b (to cut the network in half, you must cut two links) Diameter = N / 2

6. 2-D Mesh (k x k)

7. 2-D Mesh Number of Links as function of number of nodes, N : ~4N (linear) Number of connections per node: 4 (constant) Link bandwidth = speed of single link, L Total bandwidth = 4N * L Bisection bandwidth =  sqrt(N) * L Diameter = 2 * sqrt(N) - 2

8. Complete Connections

9. Number of Links as function of number of nodes, N : N*(N - 1) / 2 Number of connections per node: N - 1 Link bandwidth = speed of single link, L Total bandwidth = L * N * (N - 1) / 2 Bisection bandwidth =  (N / 2) 2 * L Diameter = 1

10. Hypercube One Dimensional

11. Two Dimensional Hypercube

12. Three Dimensional Hypercube

13. Four Dimensional Hypercube

14. d = dimensionnumber of nodes N = 2 d Number of Links as function of number of nodes, N : N * d / 2 = (N log N) / 2 Number of connections per node: d = log N Link bandwidth = speed of single link, L Total bandwidth = L * (N log N) / 2 Bisection bandwidth =  N / 2 Diameter = d = log N

15. Cube Connected Cycles Hypercube, dimension d Each Node of Hypercube is replaced by a cycle with d nodes

16. Cube Connected Cycles d = dimensionnumber of nodes N = d * 2 d Number of Links as function of number of nodes, N : 3 * N / 2 Number of connections per node: 3 Link bandwidth = speed of single link, L Total bandwidth = L * 3 * N / 2 Bisection bandwidth =  d  log N Diameter = 2 * d  2 log N

17. Tree

18. k = depthnumber of nodes N = 2 k - 1 Number of Links as function of number of nodes, N : 3 * N - 1 Number of connections per node: 3 Link bandwidth = speed of single link, L Total bandwidth = L *( 3 * N - 1) Bisection bandwidth =  1 (cut a link to the root) Diameter = 2 * k - 2  2 log N

19. Fat Tree More Channels Higher in Tree Analysis depends on channel structure