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In this paper we generalize the idea of QuickHeapsort leading to the notionof QuickXsort. Given some external sorting algorithm X, QuickXsort yields aninternal sorting algorithm if X satisfies certain natural conditions.  With QuickWeakHeapsort and QuickMergesort we present two examples for theQuickXsort-construction. Both are efficient algorithms that incur approximatelyn log n - 1.26n +o(n) comparisons on the average. A worst case of n log n +O(n) comparisons can be achieved without significantly affecting the averagecase.  Furthermore, we describe an implementation of MergeInsertion for small n.Taking MergeInsertion as a base case for QuickMergesort, we establish aworst-case efficient sorting algorithm calling for n log n - 1.3999n + o(n)comparisons on average. QuickMergesort with constant size base cases shows thebest performance on practical inputs: when sorting integers it is slower byonly 15% to STL-Introsort.

QuickXsort: Efficient Sorting with n log n - 1.399n +o(n) Comparisons on Average