An empirical study of the run-time behavior of quicksort, Shellsort and mergesort for medium to large size data

The paper describes the results of a large empirical study to measure the practical behavior of the basic versions of the popular internal sorting algorithms, Shellsort, quicksort, and mergesort, for medium to large size data and compares them with previous results. The results give running times of θ(N^1.25) for Shellsort, quicksort, and mergesort for 1000 < N < 2 × 10⁶. The study also shows that Shellsort behaves better than mergesort for 1000 < N < 150,000. However, mergesort outperforms Shellsort for N > 150,000. Quicksort outperforms both Shellsort and mergesort for all values of N > 1000. Our fits show better performance for Shellsort than the previous studies and are mostly accurate to within 2% for 1000 < N < 2 × 10⁶. The primary reason for this error seems to be related to the error in the measured data.