1. 1 Interconnection Networks

2. 2 Interconnection Networks Interconnection Network (for SIMD/MIMD) can be used for internal connections among: Processors, Memory Modules, I/O Disk Arrays Topologies of INs can be either: 1. Static networks (i.e., Mesh, Hypercube,...) are formed of point-to-point direct connections, which will not change during program execution 2. Dynamic networks (i.e., Bus, Multistage,...) are implemented with switched channels, which are dynamically configured to match communication demand in user program

3. 3 Static Interconnects Static networks use direct links which are fixed once built. Suitable for building computers where communication patterns are predictable or implementable with static connections. Example Interconnects: Linear array, Ring Mesh, Torus Hypercubes,...

4. 4 Static Interconnects Linear Array (1D Array)... 0 1 2 3 N-2 N-1 Nodes = N Routing Function - “Self routing” Is a communication process i  j (S) (D) Node i compare its ID with dest. ID if dest.ID >, send  if dest ID <, send  where every intermediate node knows where to send incoming message to destination

5. 5 Static Interconnects Linear Array (cont.) is 1-D network in which N nodes are connected by N-1 links in a line 0 1 2 3 15 14 13 12 7 6 5 4 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Ring is obtained by connecting two terminal nodes of linear array with one extra link

6. 6 Static Interconnects Mesh (2D Array) Node N = m x n Diameter = m-1+n-1 Degree = 2 (corner nodes) 3 (side nodes) Routing Function “Row-wise routing” Source compares row first (its row & Dest’s row) if Dest row <, send  4 (middle nodes) if Dest row >, send  It then compares columns (its col & Dest’s col) if Dest col >, send  if Dest col <, send  0 1 2 m-2 m-1... 0 1 n-1...

7. 7 Static Interconnects Mesh (cont.) k-D Mesh with N = n k nodes k = 2, n = 3 Torus (a variation of mesh) has a ring connection along each row & each col k = 2, n = 3

8. 8 Static Interconnects Hypercube (Binary k-cubes) k-cube is special case of k-D array (2 nodes/D) Every node is labeled k bits (x k-1 x k-2...x 1 x 0 ) Node N = 2 k Diameter = k Degree = k Communication Rule 0 1 2-cube 0 1 1 0 3-cube 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 (x k-1 x k-2...x 1 x 0 ) (y k-1 y k-2...y 1 y 0 ) 2 nodes are adjacent if they differ in exactly 1 bit n-cube can be formed by interconnecting corresponding nodes of two (n-1)-cubes 0 1 1-cube

9. 9 Static Interconnects Hypercube (cont.) Point-to-point Routing compare IDs of S & D, if S > D look at left most bit 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 S D S 101 D 000 Broadcasting (suppose from 0) Step 1 0  1 Step 2 0  2 1  3 Step 3 0  4 1  5 2  6 3  7 2 3 0 1 6 7 4 5 S

10. 10 Static Interconnects 3-D Hypercube Routing Network Routing by least significant bit (C 0 ) 000001010011100101110111 000 001 010011 100101 110111 000000 001001 010010011011 100100101101 110110111111 Routing by middle bit (C 1 ) 000000001001010010011011100100101101110110111111

11. 11 Static Interconnects Hypercube Routing Network (cont.) 000 001 010011 100101 110111 Routing by most significant bit (C 2 ) 000001010011100101110111 In general, n-D hypercube has n fns., Routing by least significant bit (C 0 ) Routing by middle bits (C 1, C 2,..., C n-2 ) Routing by most significant bit (C n-1 )

12. 12 Dynamic Interconnects For general-purpose applications, we need to use dynamic connections (which can implement all communication patterns based on program demands) Dynamic INs include Digital Buses Multistage INs Omega, Flip, Baseline Crossbar switch networks Butterfly networks Low cost High cost