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Almost sure convergence to the Quicksort process

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  • Roesler, Uwe

Abstract

The algorithm Partial Quicksort, introduced by Conrado Martínez, sorts the l smallest real numbers for a set of n different ones. It uses a splitting like Quicksort, continuing always with the leftmost list. The normalized running time Yn(t) converges with ln→t in distribution to a non degenerate limit. The finite dimensional distributions of the process Yn converge to a limit (Ragab and Roesler (2014)), called the Quicksort process. In this paper we will present the algorithm Quicksort on the fly, a version of Partial Quicksort, showing the almost sure convergence of Yn to the Quicksort process in Skorokhod metric.

Suggested Citation

  • Roesler, Uwe, 2020. "Almost sure convergence to the Quicksort process," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5290-5309.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:9:p:5290-5309
    DOI: 10.1016/j.spa.2020.03.008
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    References listed on IDEAS

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    1. Ragab, Mahmoud & Roesler, Uwe, 2014. "The Quicksort process," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1036-1054.
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