Tables should be sorted|
(on random access machines)
We consider the problem of storing an n element subset S of a universe of size m, so that membership queries (is ) 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 , then query time 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 is essentially optimal; we show that if registers may be used, query time is possible.