Abstract
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.
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Notes
- 1.
Throughout this paper, \(\lg \) denotes the logarithm to the base 2, and we ignore ceiling and floors which do not affect our results asymptotically.
- 2.
In [10], they defined the cheap comparison based on the absolute difference between the rank of operands. This corresponds to the case when input is a permutation over integers 1 to n.
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Jayapaul, V., Jo, S., Palem, K., Satti, S.R. (2023). Energy Efficient Sorting, Selection and Searching. In: Lin, CC., Lin, B.M.T., Liotta, G. (eds) WALCOM: Algorithms and Computation. WALCOM 2023. Lecture Notes in Computer Science, vol 13973. Springer, Cham. https://doi.org/10.1007/978-3-031-27051-2_16
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