Abstract

ASSTRACT. Let U1, U2,..., Ud be totally ordered sets and let V be a set of n d-dimensional vectors In U ~ X Us.. X Ud. A partial ordering is defined on V in a natural way The problem of finding all maximal elements of V with respect to the partial ordering ~s considered The computational com-plexity of the problem is defined to be the number of required comparisons of two components and is denoted by Cd(n). It is tnwal that C~(n) = n- 1 and C,~(n) < O(n 2) for d _ ~ 2 In this paper we show: (1) C2(n) = O(n logan) for d = 2, 3 and Cd(n) ~ O(n(log2n) ~-~) for d ~ 4, (2) C,t(n)> _ flog2 n!l for d _> 2 KEY WORDS AND PHRASES: maxima of a set of vectors, computattonal complexity, number of com-parisons, algorithm, recurrence CR CATEaOmES. 5.25, 5,31, 5.39 1.

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