1. CSE 8383 - Advanced Computer Architecture Week-11 April 1, 2004 engr.smu.edu/~rewini/8383

2. Contents Message Passing (Distributed Memory) Systems Static Networks Dynamic Networks

3. MIMD Distributed Memory Systems Interconnection Networks MMMM PPPP

4. Distributed Memory Multiple address spaces Communication via send & receive Synchronization via message passing

5. Interconnection Network Several IN classification criteria Several IN classification criteria Mode of operation: synchronous vs. Asynchronous Control strategy: centralized vs. decentralized Switching techniques: circuit vs. packet switching Topology: static vs. dynamic

6. Interconnection Network Taxonomy Interconnection Network Static Dynamic Bus-basedSwitch-based 1-D2-DHC SingleMultiple SSMS Crossbar

7. Static Interconnection Networks Direct links, which are fixed once built Fixed Connections, unidirectional or bi- directional Fully Connected (Completely Connected Network (CCN)) Limited Connection Network (LCN).

8. Dynamic Interconnection Networks Communication patterns are based on program demands Connections are established on the fly during program execution Multistage Interconnection Network (MIN) and Crossbar

9. Static Network Topology Linear arrays Ring (Loop) networks Two-dimensional arrays Tree networks Cube network ….

10. Static Network Analysis Graph Representation Parameters Cost Degree Diameter Fault tolerance

11. 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

12. Linear Array N nodes, N-1 edges Node Degree: Diameter: Cost: Fault Tolerance:

13. Ring N nodes, N edges Node Degree: Diameter: Cost: Fault Tolerance:

14. Chordal Ring N nodes, N edges Node Degree: Diameter: Cost: Fault Tolerance:

15. Barrwl 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

16. Barrel Shifter N = 16 Node Degree: Diameter: Cost: Fault Tolerance:

17. Tree and Star Node Degree: Diameter: Cost: Fault Tolerance:

18. 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)

19. Fully Connected 63 12 54 Node Degree: Diameter: Cost: Fault Tolerance:

20. 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

21. Hypercubes d = 0d = 1d = 2d = 3 0 1 01 00 11 10 000 001 100110 111 011 101 010

22. Hypercubes 1110 1111 1010 1011 0110 0111 0010 0011 1101 1010 1000 1001 0100 0101 0010 0000 0001 S d = 4

23. 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

24. Subcubes and Cube Fragmentation What is a subcube? Shared Environment Fragmentation Problem Is it Similar to something you know?

25. Cube Connected Cycles (CCC) k-cube  2 k nodes k-CCC from k-cube, replace each vertex of the k cube with a ring of k nodes K-CCC  k* 2 k nodes Degree, diameter  3, 2k Try it for 3-cube

26. K-ary n-Cube n = cube dimension K = # nodes along each dimension N = k n Wraparound Hupercube  binary n-cube Tours  k-ary 2-cube

27. Analysis and performance metrics static networks Performance characteristics of static networks NetworkDegree(d)Diameter(D)Cost(#link)SymmetryWorst delay Fully connected N-11N(N-1)/2Yes1 Linear Array2N-1 NoN Binary Tree3 2(  log 2 N  –1) N-1Nolog 2 N n-cubelog 2 N nN/2Yeslog 2 N 2D-Mesh42(n-1)2(N-n)No NN K-ary n-cube2n n  k/2  nNYesK x log 2 N

28. Dynamic Network Analysis Parameters: Cost: number of switches Delay: latency Blocking characteristics Fault tolerance

29. Switch Modules A x B switch module A inputs and B outputs In practice, A = B = power of 2 Each input is connected to one or more outputs (conflicts must be avoided) One-to-one (permutation) and one-to- many are allowed

30. Binary Switch 2x2 Switch Legitimate States = 4 Permutation Connections = 2