In this paper we introduce the concept of zero-change transformations to quantify the suboptimality of existing placers. Given a netlist and its placement from a placer, we formally define a class of netlist transformations that produce different netlists from the given netlist but have the same Half-Perimeter Wire Length (HPWL). Furthermore, the optimal HPWL value of the new netlists is no less than that of the original netlist. By applying our transformations and re-executing the placer, we can interpret any deviation in HPWL as a lower bound to the deviation from the optimal HPWL value. Such deviation is a measure of suboptimality. Using these transformations, the suboptimality of several existing academic and industrial placers is studied on the IBM benchmarks. Our results show that current placers are sub-optimal for zero-change transformations with deviations in HPWL by up to 32% on the IBM (version 1) benchmarks. The specific nature of our transformations also pinpoints possible directionsfor improvement in existing placers.
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