Timing-driven placement by grid-warping

Grid-warping is a recent placement strategy based on a novel physical analogy: rather than move the gates to optimize their location, it elastically deforms a model of the 2-D chip surface on which the gates have been coarsely placed via a standard quadratic solve. In this paper, we introduce a timing-driven grid-warping formulation that incorporates slack-sensitivity-based net weighting. Given inevitable concerns about wirelength and runtime degradation in any timing-driven scheme, we also incorporate a more efficient net model and an integrated local improvement ("rewarping") step. An implementation of these ideas, Warp2, can improve worst-case negative slack by 37% on average, with very modest increases in wirelength and runtime.