1. 2015-06-25 1 Global Routing Prof. Shiyan Hu shiyan@mtu.edu Office: EERC 731

2. 2 2015-06-25 Global Routing Approaches Sequential Approach –Net ordering based approach Concurrent Approach –Integer Programming

3. 3 2015-06-25 Net Ordering In sequential approach, we need some net ordering. A bad net ordering will increase the total wire length, and may even prevent completion of routing for some circuits which are indeed routable. A A B B B first (Good order) A A B B A first (Bad order)

4. 4 2015-06-25 Criteria for Net Ordering Criticality of net - critical nets first. Estimated wire length - short nets first since they are less flexible. Consider bounding rectangles (BR): A A B B B is in A’s BR

5. 5 2015-06-25 Net Ordering (cont’d)

6. 6 2015-06-25 Concurrent Approach Consider all the nets simultaneously. Formulate as an integer program. Given: L ij = Total wire length of T ij C e = Capacity of edge e Determine variable x ij s.t. x ij = 1 if T ij is used x ij = 0 otherwise. T n1, T n2,..., T nk n net n :::: :::: T 11, T 12,......, T 1k 1 net 1 Set of possible routing treesNets

7. 7 2015-06-25 Integer Program Formulation

8. 8 2015-06-25 Concurrent Approach: Example Possible trees: net 1: 233 net 2: 233 net 3: 22 1 2 3 2 1 3 1 2Solution1 2 3 2 1 3 1 2 What are the constraints for edge capacity?

9. 9 2015-06-25 Integer Programming Approach  Standard techniques to solve IP.  No net ordering. Give global optimum.  Can be extremely slow, especially for large problems.  To make it faster, a fewer choices of routing trees for each net can be used.  Determining a good set of choices of routing trees is a hard problem by itself.