Optimal redistribution of white space for wire length minimization

Existing floorplanning algorithms compact blocks to the left and bottom. Although the compaction obtains an optimal area, it may not be good to meet other objectives such as minimizing total wire length which is the first-order objective. It is not known in the literature how to place blocks to obtain an optimal wire length. In this paper, we first show that the problem can be formulated as linear programming. Thereafter, instead of using the general but slow linear programming, we propose an efficient min-cost flow based approach to solve it. Our approach guarantees to obtain the minimum of total wire length in polynomial time and meanwhile keep the minimum area by distributing white space smarter for a given floorplan topology. We also show that the approach can be easily extended to handle constraints such as fixed-frame (fixed area), IO pins, pre-placed blocks, boundary blocks, range placement, alignment and abutment, rectilinear blocks, soft blocks, one-dimensional cluster placement, and bounded net delay, without loss of optimality. Practically, the algorithm is so efficient in that it finishes in less than 0.4 seconds for all MCNC benchmarks of block placement. It is also very effective. Experimental results show we can improve 4.2% of wire length even on very compact floorplans. Thus it provides an ideal way of post-floorplanning (refine floorplanning).