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arXiv · 1307.3033

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

Stefan Edelkamp·Armin Weiß
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Abstract

In this paper we generalize the idea of QuickHeapsort leading to the notion of QuickXsort. Given some external sorting algorithm X, QuickXsort yields an internal sorting algorithm if X satisfies certain natural conditions. With QuickWeakHeapsort and QuickMergesort we present two examples for the QuickXsort-construction. Both are efficient algorithms that incur approximately n 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 average case. Furthermore, we describe an implementation of MergeInsertion for small n. Taking MergeInsertion as a base case for QuickMergesort, we establish a worst-case efficient sorting algorithm calling for n log n - 1.3999n + o(n) comparisons on average. QuickMergesort with constant size base cases shows the best performance on practical inputs: when sorting integers it is slower by only 15% to STL-Introsort.

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Stefan Edelkamp, Armin Weiß. 2013-07-11. QuickXsort: Efficient Sorting with n log n - 1.399n +o(n) Comparisons on Average. https://arxiv.org/abs/1307.3033

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