Data structures and program design (3rd ed.)
Data structures and program design (3rd ed.)
Multiple Quickselect—Hoare's Find algorithm for several elements
Information Processing Letters
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
A generating functions approach for the analysis of grand averages for multiple QUICKSELECT
proceedings of the eighth international conference on Random structures and algorithms
Communications of the ACM
Quickselect and the Dickman Function
Combinatorics, Probability and Computing
Comparisons in Hoare's Find Algorithm
Combinatorics, Probability and Computing
Note: Moves and displacements of particular elements in Quicksort
Theoretical Computer Science
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We investigate the number of swaps made by Quick Select (a variant of Quick Sort for finding order statistics) to find an element with a randomly selected rank under realistic partition algorithms such as Lomuto's or Hoare's. This kind of grand average provides a smoothing over all individual distributions for specific fixed order statistics. The grand distribution for the number of swaps (when suitably scaled) is a perpetuity (a sum of products of independent mixed continuous random variables supported on the interval (0,1)). The tool for this proof is contraction in the Wasserstein metric space, and identifying the limit as the fixed-point solution of a distributional equation. The same methodology carries over when Quick Select is commissioned to find an extremal order statistic (of a relatively small or relatively large rank) and the results are of similar nature. It is one of our purposes to show that analysis under different partition algorithms leads to different results.