Power is now a first-order design constraint in large-scale parallel computing. Used carefully, dynamic voltage scaling can execute parts of a program at a slower CPU speed to achieve energy savings with a relatively small (possibly zero) time delay. However, the problem of when to change frequencies in order to optimize energy savings is NP-complete, which has led to many heuristic energy-saving algorithms. To determine how closely these algorithms approach optimal savings, we developed a system that determines a bound on the energy savings for an application. Our system uses a linear programming solver that takes as inputs the application communication trace and the cluster power characteristics and then outputs a schedule that realizes this bound. We apply our system to three scientific programs, two of which exhibit load imbalance - particle simulation and UMT2K. Results from our bounding technique show particle simulation is more amenable to energy savings than UMT2K. (c) 2007 ACM.