Abstract
We consider the problem of storing an n element subset S of a universe of size m, so that membership queries (is x ∈ S?) can be answered efficiently. The model of computation is a random access machine with the standard instruction set (direct and indirect adressing, conditional branching, addition, subtraction, and multiplication). We show that if s memory registers are used to store S, where n ≤ s ≤ m/n ∈, then query time Ω(log n) is necessary in the worst case. That is, under these conditions, the solution consisting of storing S as a sorted table and doing binary search is optimal. The condition s ≤ m/n ∈ is essentially optimal; we show that if n+m/n o(1) registers may be used, query time o(log n) is possible.
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© 1995 Springer-Verlag Berlin Heidelberg
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Fich, F., Miltersen, P.B. (1995). Tables should be sorted (on random access machines). In: Akl, S.G., Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1995. Lecture Notes in Computer Science, vol 955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60220-8_87
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DOI: https://doi.org/10.1007/3-540-60220-8_87
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