A revisit to voltage partitioning problem

We revisit voltage partitioning problem when the mapped voltages of functional units are predetermined. If energy consumption is estimated by formulation E=CV², a published work claimed this problem was NP-hard. We clarify that it is polynomial solvable, then propose an optimal algorithm, its time complexity is O(nk+k²d) which is best so far, where n, k, and d are respectively the numbers of functional units, available supply voltages, and voltages employed in the final design. In reality, considering leakage power the energy-voltage curve is not simply monotonically increasing and there is still no optimal polynomal polynomial time algorithm. However, under the assumption that energy-voltage curve is quasiconvex, which is also a good approximation to actual situation, the optimal solution can be got in time O(nk²). Experimental results show that our algorithms are more efficient than previous works.