Determining schedules for reducing power consumption using multiple supply voltages

Dynamic power is the main source of power consumption in CMOS circuits. It depends on the square of the supply voltage. It may significantly be reduced by scaling down the supply voltage of some computational elements in the circuit, with the penalty of an increase of their execution delay. To reduce the dynamic power consumption, without degrading the performance determined assuming that the circuit operates at the highest available supply voltage, the supply voltage of computational elements off critical paths can be scaled down. Defined here as MinP_dyn, the problem of minimizing the dynamic power consumption, under performance constraints, by scaling down the supply voltage of computational elements on non-critical paths is NP-hard in general. Solving MinP_dyn for multi-phase clocked sequential circuits may allow to reduce their power consumption and the required number of registers. Reducing the number of registers also allows to reduce the power consumption, the number of control signals, and the area of the circuit. In this paper, we focus on devising methods to efficiently solve MinP_dyn for designs modeled as cyclic or acyclic graphs. More precisely, once the circuit is optimized for timing constraints, then we look for schedules that allow the computational elements of the circuit to operate at the lowest possible supply voltage. We present an integer linear programming formulation for that problem, which we use to devise a polynomial time solvable method and an exact algorithm based on a branch-and-bound technique. Experimental results confirm the effectiveness of the method and power reduction factors as high as 53.84% were obtained. Also, they show that the exact algorithm produces optimal results in a small number of tries, which is due to the rules used to prune useless solutions