George Bezerra (Department of Computer Science, University of New Mexico)
Abstract. Over 40 years of technological evolution, computer micro-architectures have scaled in size by 6 orders of magnitude, following the exponential trends dictated by Moore's law. In this process, the energy used for communication scaled faster than the energy used for computation, constraining the space of viable architectures and leading to a major transition in the way we design computers, from the monolithic to the multi-core design.
In this talk, we present Rent's rule, a power-law relationship used to model the scaling of communication in digital circuits. Rent's rule characterizes the fractal, hierarchical modular structure of logic networks and has many applications in traditional computer architecture design. Here, we show that Rent's rule can also be applied in the multi-core domain to characterize the communication patterns between cores, and use this result to model the energy consumption of parallel applications in multi-core chips.
Finally, we explore an analogy between computer chips and biological organisms and establish a theoretical relationship between Rent's rule and the WBE model from Metabolic Scaling Theory. We show that despite their striking differences in topology and function, there are strong similarities in the way complex logic circuits in chips and vascular networks in organisms scale. We further discuss the implications of these results for the development of a general theory of network scaling in complex systems.