Minimizing wire length in floorplanning

Existing floorplanning algorithms compact blocks to the left and bottom. Although the compaction obtains an optimal area, it may not be good for meeting other objectives such as minimizing the 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. This paper first shows that the problem can be formulated by linear programming. Thereafter, instead of using the general, but slow, linear programming, this paper proposes an efficient minimum-cost flow-based approach to solve it. This approach guarantees to obtain the minimum total wire length in polynomial time and meanwhile keep the minimum area by distributing white space smarter for a given floorplan topology. This paper also shows that the approach can be easily extended to handle constraints such as fixed frame (fixed area), input-output (IO) pins, preplaced 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 that it finishes in less than 0.4 s for all Microelectronics Center of North Carolina (MCNC) benchmarks of block placement. It is also very effective. Experimental results show that the wire length of very compact floorplans can even be improved by 4.2%. Thus, it provides an ideal way for postfloorplanning refinement.