Studies of Clustering Objectives and Heuristics for Improved Standard-Cell Placement

This paper describes ongoing studies of clustering objectives and heuristics, along with their e ect on top-down partitioning based standard-cell placement. Clustering for placement has three main facets { the objective, the heuristic, and the bene ts { but the connections among these facets have never been clari ed. Our studies represent the rst steps toward reconciling these three facets. Speci cally: (1) we consider seven distinct objectives (three from the literature, four new), by which we can rank given clustering heuristics; (2) we consider 35 variants of 13 clustering heuristics (four from the literature, nine new); (3) we evaluate the bene ts of given clusterings using a recent top-down partitioning based placement tool [HK97] whose approach and solution quality re ect those of leading-edge tools (e.g., quadratic top-down placers); and (4) based on these steps, we identify (new) objectives and heuristics that seem most bene cial to placement. Our paper concludes by discussing some limitations and near-term extensions to the present study. 1 Preliminaries: Clustering for Placement A clustering of a standard-cell netlist groups cells into disjoint clusters. With respect to the placement phase of physical design, there are at least three major purposes for clustering. First, clustering contracts a large problem instance into a smaller instance; this saves runtime or allows better search of the solution space, and is the primary motivation in the literature. Second, when it is known that cells should be near each other in the placement, clustering them together prevents, e.g., a top-down partitioner from making a mistake. Third, clustering can incorporate knowledge of problem structure that the placer would otherwise have to ignore (e.g., recognition of synthesized bu er-inverter trees, recognition of two-dimensional regularity [NJ96], \electrical clustering", or hierarchy-based clustering [BHB96]); we believe that this will be the key motivation for clustering in the future. In our work, we study clustering for placement in terms of three elements: the clustering objective, the clustering heuristic, and the perceived bene t to placement. The Clustering Objective. The true de nition of a good clustering is \one that leads to better placement solution quality". As noted in [AK94], this is a meta-objective, e.g., one can replace \placement" by \two-phase FM partitioning" in the de nition (see also comments by Soukup regarding placement objectives [Sou81]); it cannot be optimized by traditional methods. The key question is whether a good clustering objective, optimizable by traditional methods, can be deduced from knowledge of the placer that uses the clustering. So far, only intuitive clustering objectives have been proposed,