Wot the L: Analysis of Real versus Random Placed Nets, and Implications for Steiner Tree Heuristics.

The NP-hard Rectilinear Steiner Minimum Tree (RSMT) problem has been studied in the VLSI physical design literature for well over three decades. Fast estimators of RSMT cost (which reflects routed wirelength) are a required ingredient of modern physical planning and global placement methods. Constructive estimators build heuristic RSMTs whose costs are used as wirelength estimates; notably, these include FLUTE[8]. Analytic and lookup table-based estimators include the methods of Cheng[7] and Caldwell et al. [3]; the latter is based on both the number of points and the aspect ratio of the pointset in the RSMT instance. We observe that the physical design literature has numerous evaluations of RSMT heuristics and estimators on random pointsets, and that the relative merits of heuristics and estimators have been determined based on this use of random pointsets. In this paper, we show that a pointset attribute which we call L-ness highlights the difference between real placements and random placements of net pins. We explain why placements of netlists in practice result in pointsets with much higher L-ness than random pointsets, and we confirm this difference empirically for both academic and commercial placement tools. We further present an improved lookup table-based RSMT cost estimator that includes an L-ness parameter. Last, we illustrate how differences between Steiner tree heuristics can change depending on whether real or random pointsets are used in the evaluation.