Convergent Net Weighting Schemes in Hypergraph-based Optimization

Approaches for solving the timing-driven placement problem have traditionally been either net-based or path-based; see, e.g., [7] for an overview. Net weighting methods, which fall in the latter category, have been a popular tool in analytical placers [16, 8, 9] for handling timing-driven placement. They enjoy a number of advantages, including very low computational complexity, high flexibility, and ease of implementation – weighting algorithms can be implemented within the framework of an existing placement tool by a simple modification of the objective function. However, net weighting methods suffer the disadvantage that they are largely ad-hoc; to date there has been very little theoretical justification for their use [10]. As a result, a number of very different weighting schemes have been proposed, of which some have been shown to be effective in reducing delay. Our goal is to distill the essential properties of a robust and effective net weighting method.