Lower Bounds for Static Dictionaries on RAMs with Bit Operations But No Multiplication

We consider solving the static dictionary problem with n keys from the universe {0,..., m−1} on a RAM with direct and indirect addressing, conditional jump, addition, bitwise Boolean operations, and arbitrary shifts (a Practical RAM). For any e > 0, tries yield constant query time using space me, provided that n=m0(1). We show that this is essentially optimal: Any scheme with constant query time requires space ≥ me for some e > 0, even if n ≤ (log m)2.

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