1. Multi-Layer Channel Routing Complexity and Algorithm Rajat K. Pal

2. Chapter 4 A General Framework for Track Assignment in Multi- Layer Channel Routing Presented By- Md. Muhidul Islam Khan ID: 100705049P

3. Some Terminologies Channel: A channel is a horizontal routing area with fixed pins on the top and bottom NET: The collection of all pins with the same number is called a NET TAH Framework: Algorithm for computing reduced wire length channel routing solutions using a purely graph theoretic framework, TAH (Track Assignment Heuristic) that was designed for computing minimum area routing solutions

4. Channel Routing Terminology Upper boundary Lower boundary Tracks Terminals Via TrunksBranches Dogleg

5. Routing Layer Models HV model VH model HVH model VHV model Layer 1 Layer 2 Layer 3 Via 1 layer 2 layers 3 layers

6.  An example channel instance of ten nets  Intervals of the nets are placed in five different tracks  The length of the channel (i.e., the number of columns) is 15  Arrows indicate that the terminals to be connected, either on the top or at the bottom, to complete the required interconnection of all the nets present in the channel

7. TAH Basics The Algorithm TAH assigns intervals to tracks from top to bottom. In the first iteration the algorithm assigns a set of non-overlapping intervals to the top most track. Then it delete the nets corresponding to these intervals from the channel. In the second iteration it assigns a set of non- overlapping intervals to the second track. The iterative process continues till all the nets are assigned to tracks in the channel.

8. I2I2 I7I7 I5I5 I4I4 I1I1 I3I3 I6I6 014 5 1 670 49 10 0 23 5 2 68 9 8 70 9 35 I8I8 I9I9 I 10  The Channel contains total 10 nets  Density of this channel is ( ) is 5  Intervals of nets 1, 4, 5, 3, and 2 are overlapping to each other, and form a clique

9. I2I2 I7I7 I5I5 I4I4 I1I1 I3I3 I6I6 014 5 1 670 49 10 0 23 5 2 68 9 8 70 9 35 I8I8 I9I9 I 10 1 4 6 7 8 10 2 9 53 VCG

10. I4I4 014 5 1 670 49 10 0 23 5 2 68 9 8 70 9 35 I 10 1 6 7 8 2 9 53 VCG Track 1

11. I7I7 I1I1 014 5 1 670 49 10 0 23 5 2 68 9 8 70 9 35 6 8 2 9 53 VCG Track 2

12. I5I5 014 5 1 670 49 10 0 23 5 2 68 9 8 70 9 35 8 23 VCG Track 3 I6I6 I9I9

13. 014 5 1 670 49 10 0 23 5 2 68 9 8 70 9 35 3 VCG Track 4 I2I2 I8I8

14. 014 5 1 670 49 10 0 23 5 2 68 9 8 70 9 35 3 VCG Track 4 I2I2 I8I8

15. 014 5 1 670 49 10 0 23 5 2 68 9 8 70 9 35 Track 5 I3I3

16. Finally using TAH

17. A Two Layer No Dog-leg routing solution for Ex.2 using TAH

18. Thank You