The heap-mergesort

In this paper, we present a new mergesort algorithm which can sort n(= 2h+1 − 1) elements using no more than n log2(n+1) − (13/12)n − 1 element comparisons in the worst case. This algorithm includes the heap (fine heap) creation phase as a pre-processing step, and for each internal node v, its left and right subheaps are merged into a sorted list of the elements under that node. Experimental results show that this algorithm requires only n log2(n+1) − 1.2n element comparisons in the average case. But it requires extra space for n LINK fields.