Optimality and scalability study of existing placement algorithms

Placement is an important step in the overall IC design process in DSM technologies, as it defines the on-chip interconnects, which have become the bottleneck in determining circuit performance. The rapidly increasing design complexity, combined with the demand for the capability of handling nearly flattened designs for physical hierarchy generation, poses significant challenges to existing placement algorithms. There are very few studies on understanding the optimality and scalability of placement algorithms, due to the limited sizes of existing benchmarks and limited knowledge of optimal solutions. The contribution of this paper includes two parts: (1) we implemented an algorithm for generating synthetic benchmarks that have known optimal wirelengths and can match any given net distribution vector; (2) using benchmarks of 10K to 2M placeable modules with known optimal solutions, we studied the optimality and scalability of three state-of-the-art placers, Dragon (M. Wang et al, Proc. Int. Conf. on CAD, pp. 260-264, 2000), Capo (A.E. Caldwell et al, Proc. Design Automation Conf., pp. 477-482, 2000), mPL (K. Sze, 2002) from academia, and one leading edge industrial placer, QPlace from Cadence. For the first time our study reveals the gap between the results produced by these tools versus true optimal solutions. The wirelengths produced by these tools are 1.66 to 2.53 times the optimal in the worst cases, and are 1.46 to 2.38 times the optimal on the average. As for scalability, the average solution quality of each tool deteriorates by an additional 4% to 25% when the problem size increases by a factor of 10. These results indicate significant room for improvement in existing placement algorithms.