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A Distributional Analysis of QuickXsort for Mergesort

Authors Jasper Ischebeck , Florian Lesny, Ralph Neininger

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Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Sorting and searching
Keywords
  • QuickXsort
  • Analysis of Algorithms
  • Mergesort
  • distribution analysis
  • limit law
  • weak convergence
  • contraction method

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Abstract

QuickXsort is an efficient in situ sequential sorting algorithm that mixes Hoare’s Quicksort algorithm with another sorting algorithm X, such as Heapsort, Insertionsort or Mergesort. The advantage is that QuickXsort can be in-place even if X is not. QuickXsort works recursively like Quicksort but uses sorting algorithm X on one of the sub-lists generated in each step. While the expected complexity of QuickXsort, measured by the number of key comparisons, has been investigated for various choices of X, here the asymptotic variance and distribution of the normalized complexity are studied with Mergesort used as X. Various versions of Mergesort and splitting regimes for the decomposition of the list by Quicksort are considered and periodicities in moments and the distributions are characterized.

Cite As Get BibTex

Jasper Ischebeck, Florian Lesny, and Ralph Neininger. A Distributional Analysis of QuickXsort for Mergesort. In 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 381, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.AofA.2026.22

Author Details

Jasper Ischebeck
  • Department of Mathematics, Uppsala University, Sweden
Florian Lesny
  • Institute of Mathematics, Goethe University Frankfurt, Frankfurt a.M., Germany
Ralph Neininger
  • Institute of Mathematics, Goethe University Frankfurt, Frankfurt a.M., Germany

Funding

  • Ischebeck, Jasper: Ragnar Söderberg Foundation and Göran Gustafsson Foundation

Acknowledgements

We thank Sebastian Wild for pointing out the present problem and for addressing the subject during his plenary talk at the Analysis of Algorithms meeting 2025 in Toronto.

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