Global Routing Prof. Shiyan Hu Office: EERC 731

Global Routing Approaches Sequential Approach –Net ordering based approach Concurrent Approach –Integer Programming

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)

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

Net Ordering (cont’d)

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

Integer Program Formulation

Concurrent Approach: Example Possible trees: net 1: 233 net 2: 233 net 3: Solution What are the constraints for edge capacity?

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.