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Resilient Quicksort and Selection

  • Maxim Babenko
  • Ivan Pouzyrevsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7353)

Abstract

We consider the problem of sorting a sequence of n keys in a RAM-like environment where memory faults are possible. An algorithm is said to be δ-resilient if it can tolerate up to δ memory faults during its execution. A resilient sorting algorithm must produce a sequence where every pair of uncorrupted keys is ordered correctly. Finocchi, Grandoni, and Italiano devised a δ-resilient deterministic mergesort algorithm that runs in O(n logn + δ 2) time. We present a δ-resilient randomized algorithm (based on quicksort) that runs in \(O(n \log n + \delta \sqrt{n \log n})\) expected time and its deterministic variation that runs in \(O(n \log n + \delta \sqrt{n} \, \log n)\) worst-case time. This improves the previous known result for \(\delta > \sqrt{n} \, \log n\).

Our deterministric sorting relies on the notion of an approximate k-th order statistic. For this auxiliary problem, we devise a deterministic algorithm that runs in \(O(n + \delta \sqrt{n})\) time and produces a key (either corrupted or not) whose order rank differs from k by at most O(δ).

Keywords

Sorting Algorithm Deterministic Variation Recursion Tree Memory Fault Sorting Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Maxim Babenko
    • 1
    • 2
  • Ivan Pouzyrevsky
    • 1
    • 2
  1. 1.Moscow State UniversityRussia
  2. 2.YandexRussia

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