The approximation scheme for peak power driven voltage partitioning

With advancing technology, large dynamic power consumption has significantly limited circuit miniaturization. Minimizing peak power consumption, which is defined as the maximum power consumption among all voltage partitions, is important since it enables energy saving from the voltage island shutdown mechanism. In this paper, we prove that the peak power driven voltage partitioning problem is NP-complete and propose an efficient provably good fully polynomial time approximation scheme for it. The new algorithm can approximate the optimal peak power driven voltage partitioning solution in O(m2(mn/ε4)m) time within a factor of (1 + ε) for sufficiently small positive ε, where n is the number of circuit blocks and m is the number of partitions which is a small constant in practice. Our experimental results demonstrate that the dynamic programming cannot finish for even 20 blocks while our new approximation algorithm runs fast. In particular, varying ε, orders of magnitude speedup can be obtained with only 0.6% power increase. The tradeoff between the peak power minimization and the total power minimization is also investigated. We demonstrate that the total power minimization algorithm obtains good results in total power but with quite large peak power, while our peak power optimization algorithm can achieve on average 26.5% reduction in peak power with only 0.46% increase in total power. Moreover, our peak power driven voltage partitioning algorithm is integrated into a simulated annealing based floorplanning technique. Experimental results demonstrate that compared to total power driven floorplanning, the peak power driven floorplanning can significantly reduce peak power with only little impact in total power, HPWL, estimated power ground routing cost, level shifter cost and runtime. Further, when the voltage island shutdown is performed, peak power driven voltage partitioning can lead to over 10% more energy saving than a greedy frequency based voltage partitioning when multiple idle block sequences are considered.