On the Optimality of Some Set Algorithms

Abstract

The establishment of lower bounds on the number of comparisons necessary to solve various combinatorial problems is considered. Some of the new results are : (a) given two finite sets of real numbers, A and B, where n = max ( | A |, | B |), O(n.log n) comparisons are required to determine if A = B, even when comparisons are allowed between linear functions of the numbers; and (b) the maximum of a set of n real numbers cannot be computed in fewer than n - 1 comparisons if comparisons of only linear functions of the numbers are permitted, but the maximum can be computed in Ilog2n] comparisons if comparisons are allowed between exponential functions of the numbers. © 1972, ACM. All rights reserved.