Greatest-common-divisor dependency of juggling sequence rotation efficient performance

Abstract

Abstract In previous experimental study with three-way-reversal and juggling sequence rotation algorithms, using 20,000,000 elements for type LONG in Java, the average execution times have been shown to be 49.66761ms and 246.4394ms, respectively. These results have revealed appreciable low performance in the juggling algorithm despite its proven optimality. However, the juggling algorithm has also exhibited efficiency with some offset ranges. Due to this pattern of the juggling algorithm, the current study is focused on investigating source of the inefficiency on the average performance. Samples were extracted from the previous experimental data, presented differently and analyzed both graphically and in tabular form. Greatest common divisor values from the data that equal offsets were used. As emanating from the previous study, the Java language used for the rotation was to simulate ordering of tasks for safety and efficiency in the context of real-time task scheduling. Outcome of the investigation shows that juggling rotation performance competes favorably with three-way-reversal rotation (and even better in few cases) for certain offsets, but poorly with the rests. This study identifies the poorest performances around offsets in the neighborhood of square root of the sequence size. From the outcome, the study therefore strongly advises application developers (especially for real-time systems) to be mindful of where and how to in using juggling rotation.