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Summary: BIT31(1991).194-201.
THE RECURSIVE STRUCTURE OF
SOME ORDERING PROBLEMS
M. D. ATKINSON
School of Computer Science, Carleton University, Ottawa, Ontario, Canada KIS 5B6
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. If X(n) denotes an instance of size n of any one of these problems then X(n) can be
solved by finding the solution to a number ~(n,k) of problems X(k) for some fixed k; ~(n,k) is called the
relative 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.
AMS Classificationnumbers:06A10, 68C05
L Introduction.
Divide and conquer is one of the most useful paradigms in algorithm design. One
of its key aspects is the technique of solving a problem X(n), of size n, by making use
of solutions to problems X(k) with k < n; thus divide and conquer algorithms are
applicable for those problems whose solution can be expressed recursively. We shall
investigate, for several classical ordering problems X(n), the numberof solutions to
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