1. An ILP-based Automatic Bus Planner for Dense PCBs P. C. Wu, Q. Ma and M. D. F. Wong Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign ASPDAC 2013

2. Outline Introduction Problem Formulation Methodology  Candidate routes generation  Layer assignment  Resolving congestions  Postprocessing Experimental Results Conclusions

3. Introduction Nowadays, a dense PCB contains thousands of pins. High pin density makes manual design of PCBs an extremely time consuming task. An auto-router for PCBs would improve design productivity tremendously since each board takes about 2 months to route manually. Design automation of PCB routing becomes a necessity.

4. Introduction Bus planning: simultaneously solve the bus decomposition, escape routing, layer assignment and global bus routing.

5. Introduction If the escape directions of the buses are predetermined and bus 3 is decided to escape to the left boundary, the set of buses can no longer be routed on one layer.

6. Problem Formulation The route of a bus is composed of the escape route part and the global route part. If the escape routes of two buses conflict, we call it internal conflict. If the global routes of two buses conflict, we call it external conflict. The buses conflicting with each other have to be assigned to different layers.

7. Problem Formulation Input:  A number of components  A set of buses  The number of available routing layers Objective:  Decide the bus escape routes and decomposition (if necessary) within the components  The global routes outside the components  The layer assignment of the topological routes of buses

8. Methodology Candidate route generation  Escape routing and bus decomposition  Global routing Layer assignment  ILP formulation Resolving congestion Postprocessing

9. Methodology

10. Candidate Routes Generation Generate a collection of escape routes for all buses. A global router is applied to generate the global routes. With a number of options for escape routes and global routes, a bus may have more than one candidate route.

11. Candidate Routes Generation Escape Routing and Bus Decomposition  The boundary that a pin cluster escapes to is called escaping boundary.  A bus has two pin clusters, it has 4X4=16 combinations of escaping boundary.

12. Candidate Routes Generation Escape Routing and Bus Decomposition  If a bus fails to be escaped, then the bus is unable to be escaped on one layer and thus has to be decomposed into two or smaller buses.  Decompose a bus by iteratively applying the escape router until all pins are escaped.  For each bus, all of its candidate escape routes can be obtained by enumerating all the combinations of the escaping boundaries and rectilinear regions.

13. Candidate Routes Generation Global Routing

14. Candidate Routes Generation Global Routing

15. Candidate Routes Generation Global Routing

16. Layer Assignment ILP Formulation  Input: A set of buses {b 1, …, b m } A set of candidate routes {c 1, …, c n } p routing layers  Output: A conflict free layer assignment

17. Layer Assignment Objective: n ci : the number of the nets of a candidate route c i x il : candidate route c i assigned to layer l

18. Layer Assignment Candidate Constraints: Conflict Constraints:

19. Layer Assignment Bus Decomposition Constraints:  Suppose b 1 contains two bus decompositions, d 1 and d 2, where d 1 ={b 2, b 3, b 4 } and d 2 ={b 5, b 6 }.  Only one bus decomposition can be selected by the ILP.

20. Layer Assignment Algorithm

21. Resolving Congestions Critical Cuts  The line segments connecting each component corner to all its visible component corners or board boundaries.

22. Resolving Congestions

23. Postprocessing Improve the results by trying to reassign the unassigned buses to the routing layers. Collect the set of all unassigned buses, try to reassign them to the first layer. An ILP is formulated and solved. Try to put the new set of unassigned buses to the second layer. Such procedure is performed iteratively until no further improvement can be gained.

24. Experimental Results

25. Conclusions This paper presented an automatic bus planner, including bus decomposition, escape routing, global routing and layer assignment. The proposed planner is able to successfully route 97.4% of the nets within 2.5 hours.