Global routing by new approximation algorithms for multicommodity flow

We show how the new approximation algorithms by Garg and Konemann with extensions due to Fleischer for the multicommodity flow problem can be modified to solve the linear programming relaxation of the global routing problem. Implementation issues to improve the performance, such as a discussion of different functions for the dual variables and how to use the Newton method as an additional optimization step, are given. It is shown that not only the maximum relative congestion is minimized, but the congestion of the edges is distributed equally such that the solution is optimal in a well-defined sense: the vector of the relative congestion of the edges sorted in nonincreasing order is minimal by lexicographic order. This is an important step toward improving signal integrity by extra spacing between wires. Finally, we show how the weighted netlength can be minimized. Our computational results with recent IBM processor chips show that this approach can be used in practice even for large chips and that it is superior on difficult instances where ripup and reroute algorithms fail.