An Energy Aware Model of Computation

The design and analysis of algorithms requires a model of computation. Such a model should faithfully reflect the physical processes of computation so that a programmer can distinguish efficient computations from inefficient ones. At the same time, the model must be simple enough to be tractable and general enough to continue to apply as the underlying technologies evolve. From a computer architect’s perspective, a model of computation describes what the programmer expects, and thereby provides criteria for evaluating architectural alternatives. The models of computation that are prevalent today are based on operation counting assuming sequential program execution. These models reflect the technology of the first several decades of computing: memory accesses were as fast as ALUs so operation count determined execution time; gates were expensive but wires were cheap; the monetary cost of computing was determined by the hardware rather than the power bill. Over time, each of these assumptions have been overturned, and yet the models of computation have remained remarkably stable. This has largely been made practical through innovations in computer architecture; for example, caches and superscalar execution have hidden the cost of memory accesses. Now, the “power wall” is forcing a transition to explicitly parallel architectures and software, and traditional models of computation no longer reflect the actual costs of computation. Parallel computing offers a way around the power wall because CMOS technology allows operations to be performed with less energy by using more time. Thus, a parallel algorithm may perform more operations than its sequential counterpart, yet use less time and less energy. By combining voltage scaling, circuit design techniques and micro-architectural trade-offs, energy and time can be traded over ranges of several orders of magnitude. When these energy-time trade-offs are considered, the optimal algorithm for a task may be one that neither minimizes operation count nor computation depth. While various models have been proposed for parallel computation such as PRAMs [FW78] and logP [CKP+93], we are aware of no prior model that can address the questions that arise from the energy-time trade-offs that are at the heart of current parallel computing technologies. For example,