Timing-driven placement based on monotone cell ordering constraints

In this paper, we present a new timing-driven placement algorithm, which attempts to minimize zigzags and crisscrosses on the timing-critical paths of a circuit. We observed that most of the paths that cause timing problems in the circuit meander outside the minimum bounding box of the start and end nodes of the path. To limit this undesirable behavior, we impose a physical constraint on the placement problem, i.e., we assign a preferred signal direction to each critical path in the circuit. Starting from an initial placement solution, by using a move-based optimization strategy, these preferred directions force cells to move in a direction that maximizes the monotonic behavior of the timing-critical paths in the new placement solution. To make the direction assignment tractable, we implicitly group all circuit paths into a set of input-output conduits and assign a unique preferred direction to each such conduit. We integrated this idea into a recursive bipartitioning-based placement framework with a min-cut objective function. Experimental results on a set of standard placement benchmarks show that this approach improves the result of a state-of-the-art industrial placement tool for all the benchmark circuits while increasing the wire length by a tolerable amount.