1. Computer Science and Engineering Copyright by Hesham El-Rewini Advanced Computer Architecture

2. Computer Science and Engineering Copyright by Hesham El-Rewini Contents Dynamic Networks (Cont.) Static Networks (Revisited) Performance Analysis

3. Computer Science and Engineering Copyright by Hesham El-Rewini Multistage Interconnection Networks ISC1 ISC2 ISCn switches ISC  Inter-stage Connection Patterns

4. Computer Science and Engineering Copyright by Hesham El-Rewini Multi-stage network 000 001 010 011 100 101 110 111 000 001 010 011 100 101 110 111

5. Computer Science and Engineering Copyright by Hesham El-Rewini MIN (cont.) An 8X8 Banyan network

6. Computer Science and Engineering Copyright by Hesham El-Rewini Min Implementation Control (X) Source (S) Destination (D) X = f(S,D)

7. Computer Science and Engineering Copyright by Hesham El-Rewini Example X = 0 X = 1 ( crossed ) (straight ) A B C D A B C D

8. Computer Science and Engineering Copyright by Hesham El-Rewini Consider this MIN S1 S2 S3 S4 S5 S6 S7 S8 D1 D2 D3 D4 D5 D6 D7 D8 stage 1 stage 2 stage 3

9. Computer Science and Engineering Copyright by Hesham El-Rewini Example (Cont.) Let control variable be X 1, X 2, X 3 Find the values of X 1, X 2, X 3 to connect: S1  D6 S7  D5 S4  D1

10. Computer Science and Engineering Copyright by Hesham El-Rewini The 3 connections S1 S2 S3 S4 S5 S6 S7 S8 D1 D2 D3 D4 D5 D6 D7 D8 stage 1 stage 2 stage 3

11. Computer Science and Engineering Copyright by Hesham El-Rewini Boolean Functions X = x 1, x 2, x 3 S = s 2, s 2, s 3 D = d 1, d 2, d 3 Find X = f(S,D)

12. Computer Science and Engineering Copyright by Hesham El-Rewini Crossbar Switch M1 M2 M3 M4 M5 M6 M7 M8 P1 P2 P3 P4 P5 P6 P7 P8

13. Computer Science and Engineering Copyright by Hesham El-Rewini Analysis and performance metrics dynamic networks 0NoO(N 2 )O(1)Crossbar 0YesO(NlogN)O(logN)MIN (m-1)YesO(m)O(mN)Multiple-bus 0YesO(1)O(N)Bus Degree of FTBlockingCostDelayNetworks

14. Computer Science and Engineering Copyright by Hesham El-Rewini Static Network Analysis (Revisited) Graph Representation Parameters Cost Degree Diameter Fault tolerance

15. Computer Science and Engineering Copyright by Hesham El-Rewini Graph Review G = (V,E) -- V: nodes, E: edges Directed vs. Undirected Weighted Graphs Path, path length, shortest path Cycles, cyclic vs. acyclic Connectivity: connected, weakly connected, strongly connected, fully connected

16. Computer Science and Engineering Copyright by Hesham El-Rewini Linear Array N nodes, N-1 edges Node Degree: Diameter: Cost: Fault Tolerance:

17. Computer Science and Engineering Copyright by Hesham El-Rewini Ring N nodes, N edges Node Degree: Diameter: Cost: Fault Tolerance:

18. Computer Science and Engineering Copyright by Hesham El-Rewini Chordal Ring N nodes, N edges Node Degree: Diameter: Cost: Fault Tolerance:

19. Computer Science and Engineering Copyright by Hesham El-Rewini Barrel Shifter Number of nodes N = 2 n Start with a ring Add extra edges from each node to those nodes having power of 2 distance i & j are connected if |j-i| = 2 r, r = 0, 1, 2, …, n-1

20. Computer Science and Engineering Copyright by Hesham El-Rewini Mesh and Torus Node Degree: Internal  4 Other  3, 2 Diameter: 2(n-1) N = n*n Node Degree: 4 Diameter: 2* floor(n/2)

21. Computer Science and Engineering Copyright by Hesham El-Rewini Hypercubes N = 2 d d dimensions (d = log N) A cube with d dimensions is made out of 2 cubes of dimension d-1 Symmetric Degree, Diameter, Cost, Fault tolerance Node labeling – number of bits

22. Computer Science and Engineering Copyright by Hesham El-Rewini Hypercubes d = 0d = 1d = 2d = 3 0 1 01 00 11 10 000 001 100110 111 011 101 010

23. Computer Science and Engineering Copyright by Hesham El-Rewini Hypercubes 1110 1111 1010 1011 0110 0111 0010 0011 1101 1010 1000 1001 0100 0101 0010 0000 0001 S d = 4

24. Computer Science and Engineering Copyright by Hesham El-Rewini Hypercube of dimension d N = 2 d d = log n Node degree = d Number of bits to label a node = d Diameter = d Number of edges = n*d/2 Hamming distance! Routing