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On the distribution of comparisons in sorting algorithms

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Abstract

We considered the following natural conjecture: For every sorting algorithm every key will be involved inΩ(logn) comparisons for some input. We show that this is true for most of the keys and prove matching upper and lower bounds. Every sorting algorithm for some input will involven−n ε/2+1 keys in at leastεlog2 n comparisons,ε>0. Further, there exists a sorting algorithm that will for every input involve at mostn−n ε/c keys in greater thanεlog2 n comparisons, wherec is a constant andε>0. The conjecture is shown to hold for “natural” algorithms from the literature.

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Author notes

  1. Pravin Vaidya

    Present address: AT&T Bell Laboratories, 07974, Murray Hill, NJ

Authors and Affiliations

  1. Dept. of Computer Science, University of Virginia, 22903, Charlottesville, VA, USA

    Dana Richards & Pravin Vaidya

  2. Dept. of Computer Science, University of Illinois, 61801, Urbana, IL, USA

    Dana Richards & Pravin Vaidya

Authors
  1. Dana Richards
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  2. Pravin Vaidya
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Richards, D., Vaidya, P. On the distribution of comparisons in sorting algorithms. BIT 28, 764–774 (1988). https://doi.org/10.1007/BF01954896

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  • DOI: https://doi.org/10.1007/BF01954896

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