1. A Negotiated Congestion based Router for Simultaneous Escape Routing Q.Ma, T.Yan and Martin D.F. Wong Department of Electrical and Computer Engineering University of Illionis at Urbana- Champaign, USA ISQED 2010

2. Outline Introduction Problem Formulation Underlying Routing Graph Negotiated Congestion Application on Bus Untangling Experimental Results Conclusion

3. Introduction PCB routing is the problem of determining wiring connections between pin terminals on the circuit board. This paper focuses on a key problem in PCB routing called escape routing. The objective of escape routing is to route all terminal pins inside a component to the component boundaries.

4. Introduction There are several types of escape routing problems:  Single-component escape: route all pins inside a component to the component boundary without any constraint on the pin ordering  Ordered escape: one component, require the escape routing to conform to specified ordering along the boundary  Simultaneous escape: two components, the pin orderings of the escape routing for the two components are required to match each other in order to provide a planar topology for later detail routing between the components

5. Introduction

6. Problem Formulation Each routing tile has a horizontal capacity, vertical capacity and a diagonal capacity. cap(2,2,3) denotes the horizontal, vertical and diagonal capacities of a tile are 2, 2 and 3.

7. Problem Formulation Input:  Two components and the net number n, each component is a rectangular pin grid Objective:  Obtain detailed routing from these pins to the boundaries so that ordering of the escaped pins along two components’ boundaries match each other.  The escape routing inside the components is also required to satisfy the capacity constraints.

8. Underlying Routing Graph Graph model for a tile  Each node in this graph model can only accommodate one net. (the node capacity is 1)

9. Underlying Routing Graph cap(2,2,3)

10. Underlying Routing Graph This graph model correctly captures cap(2,2,3)

11. Underlying Routing Graph It can be easily modified to model the tile with cap(2,2,4)

12. Underlying Routing Graph The entire routing graph

13. Negotiated Congestion The negotiated congestion based routing scheme has been widely used in FPGA routing and global routing. In this routing scheme, routability is achieved by forcing all the nets to negotiate for a resource. Determine which net needs the resource most.

14. Negotiated Congestion The cost of a node v is computed by the following formula: b v : the base cost h v : the history cost p v : the number of nets currently occupying node v

15. Negotiated Congestion Initialize the cost Increase the history cost by Δ Every net is rip-up and reroute Increase Δ

16. Application on Bus Untangling Bus untangling problem: Given two columns of pins with labels {1..n} on each column Detour the pins to make the ordering match in the middle. The detouring must also satisfy the capacity requirement between adjacent pins in each column.

17. Application on Bus Untangling Two sides untangling can redistribute the occupied vertical tracks to two sides so that the max number of vertical tracks used on one side is reduced.

18. Application on Bus Untangling Some inputs may not have single detour solutions. 3 4 2 13 4 2 1 3 4 2 13 4 2 1

19. Application on Bus Untangling View the bus untangling problem as a special case of the escape routing problem. Each pin column constitutes a component. Since NCER allows detours anywhere, the solution can have detours on both sides.

20. Experimental Results

23. Conclusion This paper studies the feasibility of applying negotiated congestion routing scheme to simultaneous escape routing problems. The two routers exhibit complementary behaviors.