Generalized heapsort

Abstract

The efficiency and mathematical approach of the Generalized Heapsort have been described. If an appropriate value of p is chosen, which in most cases is 4≤p≤6, the sorting time can be minimized.

The Generalized Heapsort, however, does not change the order of computing complexity of the Heapsort, which remains O(nlogn).

The algorithm of the Generalized Heapsort is not particularly complicated. It requires only a few modifications to the original algorithm. It is the fastest algorithm yet reported which does not require extra memory space. The Quicksort is faster on average than the Generalized Heapsort, but it has several demerits which have mentioned above. In general, the Heapsort, not only the Basic Heapsort but also the Generalized Heapsort shows a very stable response to any data condition, even data are sequentially or reversely ordered.

The numbers of key comparisons and record moves in the worst case have been described mathematically. However, the author has not yet succeeded in finding their mathematical averages. As stated above, the differences between the averages and maximum values are very small. Therefore, for examination or for comparison with other sorting algorithms, the maximum values are fairly useful.

The Generalized Heapsort algorithm is effective when data volumes are very large and also the ratio of comparison time to move time is large. However, if the move time is very much longer than the comparison time, another sorting algorithms, for instance the “key sort” should be used.