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Derivation of Randomized Sorting and Selection Algorithms

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Parallel Algorithm Derivation and Program Transformation

Part of the book series: The Springer International Series In Engineering and Computer Science ((SECS,volume 231))

Abstract

In this paper we systematically derive randomized algorithms (both sequential and parallel) for sorting and selection from basic principles and fundamental techniques like random sampling. We prove several sampling lemmas which will find independent applications. The new algorithms derived here are the most efficient known. From among other results, we have an efficient algorithm for sequential sorting.

The problem of sorting has attracted so much attention because of its vital importance. Sorting with as few comparisons as possible while keeping the storage size minimum is a long standing open problem. This problem is referred to as ‘the minimum storage sorting’ [10] in the literature. The previously best known minimum storage sorting algorithm is due to Frazer and McKellar [10]. The expected number of comparisons made by this algorithm is n log n + O(n log log n). The algorithm we derive in this paper makes only an expected n log n + O(n ω(n)) number of comparisons, for any function ω(n) that tends to infinity. A variant of this algorithm makes no more than n log n + O(n log log n) comparisons on any input of size n with overwhelming probability.

We also prove high probability bounds for several randomized algorithms for which only expected bounds have been proven so far.

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Author information

Authors and Affiliations

  1. Dept. of CIS, University of Pennsylvania, USA

    Sanguthevar Rajasekaran

  2. Dept. of Computer Science, Duke University, USA

    John H. Reif

Authors
  1. Sanguthevar Rajasekaran
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  2. John H. Reif
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Editor information

Editors and Affiliations

  1. New York University, USA

    Robert Paige

  2. Duke University, USA

    John Reif

  3. Office of Naval Reserach, USA

    Raplh Watcher

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© 1993 Kluwer Academic Publishers

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Rajasekaran, S., Reif, J.H. (1993). Derivation of Randomized Sorting and Selection Algorithms. In: Paige, R., Reif, J., Watcher, R. (eds) Parallel Algorithm Derivation and Program Transformation. The Springer International Series In Engineering and Computer Science, vol 231. Springer, Boston, MA. https://doi.org/10.1007/978-0-585-27330-3_6

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  • DOI: https://doi.org/10.1007/978-0-585-27330-3_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-9362-7

  • Online ISBN: 978-0-585-27330-3

  • eBook Packages: Springer Book Archive

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