Static Dictionaries on AC0 RAMs: Query Time Theta(sqrt(log n/log log n)) is Necessary and Sufficient
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چکیده
In this paper we consider solutions to the static dictionary problem on ACo RAMs, i.e. random access machines where the only restriction on theJinite instruction set is that all computationcil instructions are in ACO. Our main result is a tight upper and lower bound of 0 (Jlog n / log log n ) on the time for (answering membership queries in a set of size n when reasonable space is used for the data structure storing the set; the upper bound can be obtained using O(n) space, and the lower bound holds even if we allow Several varitztions of this result are also obtained. Among others, we show a tradeoff between time and circuit depth under the unit-cost assumption: any RAM instruction set which purrtits a linear space, constant query time solution to the static dictionary problem must have an instruction of depth R(1og w / log log w), where w is the word size of the machine (and log the size ofthe universe). This matches the depth of multiplication and integer division, used in the perfect hashing scheme by Fredman, Komlds and Szemerkdi. space 2 PolYlog *.
منابع مشابه
Dictionaries on AC 0 RAMs : Query Time Θ ( √ log n / log log n ) is Necessary and Sufficient
In this paper we consider solutions to the dictionary problem on AC RAMs, i.e. random access machines where the only restriction on the finite instruction set is that all computational instructions are in AC. Our main result is a tight upper and lower bound of Θ( √ log n/ log log n) on the time for answering membership queries in a set of size n when reasonable space is used for the data struct...
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