1. B-Escape: A Simultaneous Escape Routing Algorithm Based on Boundary Routing L. Luo, T. Yan, Q. Ma, M. D.F. Wong and T. Shibuya Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign ISPD 2010

2. Outline Introduction Boundary Routing Dynamic Net Ordering Application to PCB Routing Experimental Results Conclusion

3. Introduction PCB routing problem has become extremely difficult due to:  Rapid increase in pin count and density  Presence of differential pairs  Length-matching requirements This paper focuses on a key problem in PCB routing called escape routing The objective of escape routing is to route all terminal pins to the components

4. Introduction Simultaneous 2-component escape routing problem

5. Introduction This paper limits the discussion to 1-side escape 4-side escape can always be transformed into 1- side escape by adding more rows or columns

6. Boundary Routing Fixed-ordering escape problem:  The ordering of the routes must be increasing along the right side from top to bottom

7. Boundary Routing Define the routing boundary as the boundary of the maximum routable region for the unrouted pins

8. Boundary Routing A routing path is said to be monotonic if the intersection of any vertical line with the routing path is either empty, or a single point

9. Boundary Routing Upward mode: route the pin straight up until it meets the boundary and then follow the boundary clockwise

10. Boundary Routing

11. Six routing modes

12. Boundary Routing Many routing solutions that seem complex can be captured by one of the six modes

13. Dynamic Net Ordering It is very difficult to get the correct ordering A slight difference in the ordering can cause huge difference in routability

14. Dynamic Net Ordering Define the routing cost as a 2-element vector (α,β) α is the number of pins trapped (unroutable) by routing current net β is the number of pins blocked (but still routable) by current routing The cost vectors are compared with each other in lexicographical order

15. Dynamic Net Ordering Trail route Pick the net with min cost Actually route Detect the trap and get a new ordering

16. Dynamic Net Ordering Backtrack and reorder |cost(c)-cost(e)| |cost(b)-cost(d)| |cost(a)-cost(c)|

17. Application to PCB Routing

19. A differential pair is a pair of nets that are required to be routed together The routing of a DP is called pair routing

20. Application to PCB Routing

21. Experimental Results

24. Conclusion This paper presented a new simultaneous escape routing algorithm Each net is routed by a boundary routing engine and therefore guarantees great routability