Sorting N-Elements Using Natural Order: A New Adaptive Sorting Approach

Problem statement: Researchers focused their attention on optimally adaptive sorting algorithm and illustrated a need to develop tools for constructing adaptive algorithms for large classes of measures. In adaptive sorting algorithm the run time for n input data smoothly varies from O(n) to O(nlogn), with respect to several measures of disorder. Questions were raised whether any approach or technique would reduce the run time of adaptive sorting algorithm and provide an easier way of implementation for practical applications. Approach: The objective of this study is to present a new method on natural sorting algorithm with a run time for n input data O(n) to O(nlogm), where m defines a positive value and surrounded by 50% of n. In our method, a single pass over the inputted data creates some blocks of data or buffers according to their natural sequential order and the order can be in ascending or descending. Afterward, a bottom up approach is applied to merge the naturally sorted subsequences or buffers. Additionally, a parallel merging technique is successfully aggregated in our proposed algorithm. Results: Experiments are provided to establish the best, worst and average case runtime behavior of the proposed method. The simulation statistics provide same harmony with the theoretical calculation and proof the method efficiency. Conclusion: The results indicated that our method uses less time as well as acceptable memory to sort a data sequence considering the natural order behavior and applicable to the realistic researches. The parallel implementation can make the algorithm for efficient in time domain and will be the future research issue.