A Novel Blockage-avoiding Macro Placement Approach for 3D ICs based on POCS

Although the 3D integrated circuit (IC) placement problem has been studied for many years, few publications devoted to the macro legalization. Due to large sizes of macros, the macro placement problem is harder than cell placement, especially when preplaced macros exist in a multi-tier structure. In order to have a more global view, this paper proposes the partitioning-last macro-first flow to handle 3D placement for mixed-size designs, which performs tier partitioning after placement prototyping and then legalizes macros before cell placement. A novel two-step approach is proposed to handle 3D macro placement. The first step determines locations of macros in a projection plane based on a new representation, named K-tier Partially Occupied Corner Stitching. It not only can keep the prototyping result but also guarantees a legal placement after tier assignment of macros. Next, macros are assigned to respective tiers by Integer Linear Programming (ILP) algorithm. Experimental results show that our design flow can obtain better solutions than other flows especially in the cases with more preplaced macros.