A Parallel Integer Programming Approach to Global Routing

We propose a parallel global routing algorithm that concurrently processes routing subproblems corresponding to rectangular subregions covering the chip area. The algorithm uses at it core an existing integer programming (IP) formulation-both for routing each subproblem and for connecting them. Concurrent processing of the routing subproblems is desirable for effective parallelization. However, achieving no (or low) overflow global routing solutions without strong, coordinated algorithmic control is difficult. Our algorithm addresses this challenge via a patching phase that uses IP to connect partial routing solutions. Patching provides feedback to each routing subproblem in order to avoid overflow, later when attempting to connect them. The end result is a flexible and highly scalable distributed algorithm for global routing. The method is able to accept as input target runtimes for its various phases and produce high-quality solution within these limits. Computational results show that for a target runtime of 75 minutes, running on a computational grid of few hundred CPUs with 2GB memory, the algorithm generates higher quality solutions than competing methods in the open literature.