1. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Shared versus Switched Media

2. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-D Meshes

3. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Evaluating 2-D Meshes Diameter:  (n 1/2 ) Diameter:  (n 1/2 ) Bisection width:  (n 1/2 ) Bisection width:  (n 1/2 ) Number of edges per switch: 4 Number of edges per switch: 4 Constant edge length? Yes Constant edge length? Yes

4. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Binary Tree Network Indirect topology Indirect topology n = 2 d processor nodes, 2n-1 switches n = 2 d processor nodes, 2n-1 switches

5. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Evaluating Binary Tree Network Diameter: 2 log n Diameter: 2 log n Bisection width: 1 Bisection width: 1 Edges / node: 3 Edges / node: 3 Constant edge length? No Constant edge length? No

6. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Hypertree Network Indirect topology Indirect topology Shares low diameter of binary tree Shares low diameter of binary tree Greatly improves bisection width Greatly improves bisection width From “front” looks like k-ary tree of height d From “front” looks like k-ary tree of height d From “side” looks like upside down binary tree of height d From “side” looks like upside down binary tree of height d

7. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Hypertree Network

8. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Evaluating 4-ary Hypertree Diameter: log n Diameter: log n Bisection width: n / 2 Bisection width: n / 2 Edges / node: 6 Edges / node: 6 Constant edge length? No Constant edge length? No

9. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Butterfly Network Indirect topology Indirect topology n = 2 d processor nodes connected by n(log n + 1) switching nodes n = 2 d processor nodes connected by n(log n + 1) switching nodes

10. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Butterfly Network Routing

11. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Evaluating Butterfly Network Diameter: log n Diameter: log n Bisection width: n / 2 Bisection width: n / 2 Edges per node: 4 Edges per node: 4 Constant edge length? No Constant edge length? No

12. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Hypercube Direct topology Direct topology 2 x 2 x … x 2 mesh 2 x 2 x … x 2 mesh Number of nodes a power of 2 Number of nodes a power of 2 Node addresses 0, 1, …, 2 k -1 Node addresses 0, 1, …, 2 k -1 Node i connected to k nodes whose addresses differ from i in exactly one bit position Node i connected to k nodes whose addresses differ from i in exactly one bit position

13. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Hypercube Addressing

14. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Hypercubes Illustrated

15. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Evaluating Hypercube Network Diameter: log n Diameter: log n Bisection width: n / 2 Bisection width: n / 2 Edges per node: log n Edges per node: log n Constant edge length? No Constant edge length? No