Optimal placement by branch-and-price

Circuit placement has a large impact on all aspects of performance; speed, power consumption, reliability, and cost are all affected by the physical locations of interconnected transistors. The placement problem is NP-complete for even simple metrics. In this paper, we apply techniques developed by the operations research (OR) community to the placement problem. Using an integer programming (IP) formulation and by applying a "branch-and-price" approach, we are able to optimally solve placement problems that are an order of magnitude larger than those addressed by traditional methods. Our results show that suboptimality is rampant on the small scale, and that there is merit in increasing the size of optimization windows used in detail placement.