Title: Force-Directed Placement for Mixed-Size Designs

Modern placement problems consist of a combination of both standard cells and larger macro blocks which may occupy a sizeable portion of the placement area. As a result, there is a current trend toward combining floor-planning and placement together into a single step; i.e., a trend toward "floor-placement" in which all blocks and cells are placed simultaneously. Force-directed methods are somewhat generic and therefore capable of handling, somewhat seamlessly, mixed-sized designs. Hence, these methods offer one potential approach for the floor-placement problem. Unfortunately, force-directed placers are difficult to implement, and obtaining state-of-the-art results can be illusive. In this talk, we describe the implementation of a force-directed placer and specifically highlight some of the necessary details of the implementation; namely (1) computation of spreading forces, (2) potential for numerical instabilities and methods to avoid such instabilities, (3) metrics for measuring the distribution of area throughout the placement region, and (4) complementary techniques to aid in objective function minimization. The aforementioned implementation provides results comparable to other state-of-the-art placers based on min-cut partitioning and/or simulated annealing when measured in terms of wire length. Finally, we present some recent results from a multi-level flow (and other enhancements to the underlying algorithms) that offer up to a further 14% improvement in wire length when compared to the original force-directed placer.