Energy efficient sorting, selection and searching

In this paper, we introduce a model for studying energy efficient algorithms by extending the well-studied comparison model. In our model, the result of a comparison is determined based on two parameters: (i) the energy used to perform a comparison, and (ii) the absolute difference between the two values being compared – thus introducing an energy-accuracy trade-off. This model also extends the ideas presented by Geissmann and Penna [SOFSEM 2018] and Funke et al. [Comput. Geom. 2005] wherein they use two distinct types of comparisons namely low and full-energy (cheap and expensive) comparisons, by introducing multiple types of comparisons. In this extension, the accuracy of a comparison becomes a function of the energy used. We consider the fundamental problems of (i) sorting (ii) selection (iii) searching, and design efficient algorithms for these problems in the new model. We also present lower bounds on the energy usage for some of these problems, showing that some of our algorithms are asymptotically optimal with respect to the energy usage.