Abstract
Some classical ordering problems (sorting, finding the maximum, finding the maximum and the minimum, finding the largest and the next largest, merging, and finding the median) are considered from a recursive viewpoint. IfX(n) denotes an instance of sizen of any one of these problems thenX(n) can be solved by finding the solution to a number ξ(n,k) of problemsX(k) for some fixedk; ξ(nk,k) is called therelative complexity. Upper and lower bounds on the relative complexity are found. For the problem of finding the maximum, finding the maximum and the minimum, and finding the largest and the next largest these bounds are optimal.
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Atkinson, M.D. The recursive structure of some ordering problems. BIT 31, 194–201 (1991). https://doi.org/10.1007/BF01931280
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DOI: https://doi.org/10.1007/BF01931280