Efficiency of a Good But Not Linear Set Union Algorithm

Abstract

TWO types of instructmns for mampulating a family of disjoint sets which partitmn a umverse of n elements are considered FIND(x) computes the name of the (unique) set containing element x UNION(A, B, C) combines sets A and B into a new set named C. A known algorithm for implementing sequences of these mstructmns is examined It is shown that, if t(m, n) as the maximum time reqmred by a sequence of m ≥ n FINDs and n — 1 intermixed UNIONs, then kima(m, n) ≤ t(m, n) ≤ k2ma(m, n) for some positive constants ki and k2, where a(m, n) is related to a functional inverse of Ackermann's functmn and as very slow-growing. © 1975, ACM. All rights reserved.