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This paper considers the problem of merging sets formed from a total of n items in such a way that at any time, the name of a set containing a given item can be ascertained. Two algorithms using different data structures are discussed. The execution times of both algorithms are bounded by a constant times nG (n), where G (n) is a function whose asymptotic growth rate is less than that of any finite number of logarithms of n.
Hopcroft et al. (Sat,) studied this question.