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Average Cost of QuickXsort with Pivot Sampling

Author Sebastian Wild

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Author Details

Sebastian Wild
  • University of Waterloo, Canada

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada and the Canada Research Chairs Programme.

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Sebastian Wild. Average Cost of QuickXsort with Pivot Sampling. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 36:1-36:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.AofA.2018.36

Abstract

QuickXsort is a strategy to combine Quicksort with another sorting method X so that the result has essentially the same comparison cost as X in isolation, but sorts in place even when X requires a linear-size buffer. We solve the recurrence for QuickXsort precisely up to the linear term including the optimization to choose pivots from a sample of k elements. This allows to immediately obtain overall average costs using only the average costs of sorting method X (as if run in isolation). We thereby extend and greatly simplify the analysis of QuickHeapsort and QuickMergesort with practically efficient pivot selection, and give the first tight upper bounds including the linear term for such methods.

Subject Classification

ACM Subject Classification
  • Theory of computation → Sorting and searching
Keywords
  • in-situ sorting
  • constant-factor optimal sorting
  • pivot sampling
  • QuickMergesort
  • QuickHeapsort
  • Quicksort recurrence
  • average-case analysis

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