Partitioning around roadblocks: tackling constraints with intermediate relaxations

Constraint satisfaction during partitioning and placement of VLSI circuits is an important problem, and effective techniques to address it lead to high-quality physical design solutions. This problem has, however, been cursorily treated in previous partitioning and placement research. Our work presented here addresses the balance-ratio constraint, and is a crucial first step to an effective solution to the general constraint-satisfaction problem. In current iterative-improvement mincut partitioners, the balance-ratio constraint is tackled by disallowing moves that violate it. These methods can lead to sub-optimal solutions since the process is biased against the movement of large cells and clusters of cells. We present techniques for an informed relaxation process that attempts to estimate whether relaxing the constraint temporarily will ultimately benefit the mincut objective. If so, then a violating move is allowed, otherwise it is disallowed. The violations are corrected in future moves so that the final solution satisfies the given constraint. On a set of ACM/SIGDA PROUD benchmark circuits with actual cell sizes, we obtained up to 38% and an average of 14.5% better cutsizes with as little as 13% time overhead using our techniques compared to the standard method of not allowing any relaxation.