BIT31(1991).194-201. THE RECURSIVE STRUCTURE OF 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 Collections: Computer Technologies and Information Sciences