1. MAPPING OF ONE MODEL INTO OTHER MODEL Submitted by:- RATIKA AGARWAL M.Tech.-CSE

2. Embedding: Relationship between two networks G(V,E)  G’(V’,E’) Graph G, G’ Vertices V, V’ Edges E, E’ MAP E E’ V  V’

3. Process Mapping (Eg.- 2-d Mesh) Underlying Architecture Processes and their interactions Mapping of Processes to nodes

6. Types of network topologies: (Hypercube) 2-d Hypercube 0-d Hypercube 1-d Hypercube 3-d Hypercube 4-d Hypercube

8. 2-D Mesh in a Hypercube.

9. Linear Array in a 2-D Mesh.

10. 2-D Mesh in a Linear Array. And more…

11. Metrics used forEmbedding: DILATION CONGESTION EXPANSION

15. MAPPING

16. Linear Array/Ring into Hypercube MAP Linear Array 2d nodes d-dimesional Hypercube Node ‘i’ Node G(i,d) G(i, d) : Gray code of ith node of Array. RGC : Binary Reflected Gray Code. G(0,1) = 0 G(1,1) = 1 G(i,x) for i<2x G(i,x+1) 2x + G[ (2x+1 –1)-i, x] for i>= 2x

17. Example: Say d = 3 2d = 23= 8, i.e., 8 nodes in ring and hypercube.

18. Gray Coding ALTERNATIVE METHOD 3 bit RGC 2 bit RGC 1 bit RGC 0 1 2 3 4 5 6 7 0 0 0 0 00 1 0 1 0 01 1 1 0 11 1 0 0 10 1 10 1 11 1 01 1 00 G(0,1) = 0 G(1,1) = 1 Congestion=1 Dilation=1 <Mapped Model>

19. Gray Coding ALTERNATIVE METHOD 3 bit RGC 2 bit RGC 1 bit RGC 0 1 2 3 4 5 6 7 0 0 0 0 00 1 0 1 0 01 1 1 0 11 1 0 0 10 1 10 1 11 1 01 1 00 G(0,1) = 0 G(1,1) = 1 Congestion=1 Dilation=1 <Mapped Model>

22. Same column of Mesh  ‘s’ identical LSBs in mapped node00 00 01 00 11 00 10 00 10 11 10 10 10 01

23. Linear Array into 2-D Mesh MAP 16 node linear array 2-d Mesh Solid lines: links in array Normal lines: links in the mesh Congestion=1

25. To minimize the communication overhead of a parallel algorithm.

26. Laying out circuits on chips.

27. Reasons for embedding:

28. An algorithm can run on many architecture.

29. Algorithm mapped on interconnection network to achieve maximum parallelism.THANK YOU