An energy complexity model for algorithms

Abstract

Energy consumption has emerged as first class computing resource for both server systems and personal computing devices. The growing importance of energy has led to rethink in hardware design, hypervisors, operating systems and compilers. Algorithm design is still relatively untouched by the importance of energy and algorithmic complexity models do not capture the energy consumed by an algorithm.In this paper, we propose a new complexity model to account for the energy used by an algorithm. Based on an abstract memory model (which was inspired by the popular DDR3 memory model and is similar to the parallel disk I/O model of Vitter and Shriver), we present a simple energy model that is a (weighted) sum of the time complexity of the algorithm and the number of "parallel" I/O accesses made by the algorithm. We derive this simple model from a more complicated model that better models the ground truth and present some experimental justification for our model. We believe that the simplicity (and applicability) of this energy model is the main contribution of the paper.We present some sufficient conditions on algorithm behavior that allows us to bound the energy complexity of the algorithm in terms of its time complexity (in the RAM model) and its I/O complexity (in the I/O model). As corollaries, we obtain energy optimal algorithms for sorting (and its special cases like permutation), matrix transpose and (sparse) matrix vector multiplication.

On Energy Optimization in Cryptographic Hash Functions and Symmetric Key Protocols

“…The second is symmetric key encryption in which we cover Blowfish, DES, 3DES, and AES ciphers. Our work experimentally validates the applicability of the energy model proposed in [1] on these classes of cryptographic protocols. We also present a generic way to achieve any desired degree of memory parallelism for a given protocol (hash or symmetric key), which can be employed by software engineers to implement energy efficient cryptographic protocols.…”

“…(2) How do we modify existing cryptographic protocols to make them energy optimal?". The main impediment for pursuing this direction is a to prove the applicability of a realistic model of energy consumption at the algorithm design by [1] on some of these protocols. We believe that our work will complement this body of existing work.…”

“…An asymptotic energy complexity model for algorithms was proposed in [1]. Inspired by the popular DDR3 architecture, the model assumes that the memory is divided into P banks (M 1 , M 2 , · · · , M P ) each of which can store multiple blocks of size B.…”

“…But P blocks in P different memory banks can be accessed in parallel. The main contribution of the model in [1] was to highlight the effect of parallelizability of the memory accesses in energy consumption. In particular, the energy consumption of an algorithm was derived as the weighted sum T + (PB) · I, where T is the total time taken and I is the number of parallel I/Os made by the algorithm.…”

“…As mentioned, we have considered two classes of cryptographic protocols to implement a parallelism technique based on the energy model of [1] that leads to reduction in their energy consumption.…”