  The article investigates the relationship between time complexity and energy
consumption in sorting algorithms, focusing on commonly-used algorithms
implemented in Java: Bubble Sort, Counting Sort, Merge Sort, and Quick Sort.
The significance of understanding this relationship is driven by the increasing
energy demands of Information and Communication Technology systems and the
potential for software optimization to contribute to energy efficiency. If we
find a strong correlation between time complexity and energy usage, it would
enhance the ability of software developers to create energy-efficient
applications.
  This quantitative study researches the execution of four selected sorting
algorithms with input varying over input sizes (25000 to 1 million) and input
order types (best, worst, and random cases) on a single kernel in a
Java-enabled system. The input size is adjusted according to the type's maximum
execution time, resulting in 136 combinations, totalling 12960 measurements.
Wall time and the CPU energy consumption is measured using Intel's RAPL.
Statistical analysis are used to examine the correlations between time
complexity, wall time, and energy consumption.
  The study finds a strong correlation between time complexity and energy
consumption for the sorting algorithms tested. More than 99% of the variance in
energy consumption for Counting Sort, Merge Sort, and Quick Sort depend on
their time complexities. More than 94% of the variance in energy consumption
for Bubble Sort depends on its time complexity. The results affirm that time
complexity can serve as a reliable predictor of energy consumption in
sequential sorting algorithms. This discovery could guide software developers
in choosing energy-efficient algorithms by considering time complexities.
