Incremental improvement of voltage assignment

Design for low power has become a key requirement in today's System-on-a-Chip design, particularly for mobile applications. Multi-Vdd (MSV) is an effective method to reduce both leakage and dynamic powers. In a MSV design, cells of different supply voltages are often grouped into a small number of voltage islands, in order to avoid complex power-supply system and excessive amount of level shifters. In 2005, Wu proposed an elegant algorithm for voltage-island grouping based on the physical proximity of the critical cells in a postplacement voltage assignment and, in 2006, proposed an efficient algorithm for voltage assignment which not only meets timing but also forms good proximity of the critical cells. However, due to insufficient slack, a few isolated critical cells (called outliers) may still exist in the resulting voltage assignment, causing disproportionately expensive penalty to the final voltage-island grouping. In this paper, we propose a novel approach to improve the voltage assignment by automatic outlier detection followed by incremental placement. The outlier detection is based on a modified algorithm for the facility-location problem and proper parameter setting. We also propose a novel partial-sort technique which speeds up this algorithm significantly (up to 3$\times$ in our experiments). The incremental placement is guided by setting proper constraints on the paths containing the detected outliers, such that the outliers can be eliminated later. Our experiments on industry designs show that our algorithm leads to 12%54% improvement in the final voltage-island grouping, with quick turn-around time.