Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Membership in Constant Time and Almost-Minimum Space
SIAM Journal on Computing
On the cell probe complexity of membership and perfect hashing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Low Redundancy in Static Dictionaries with O(1) Worst Case Lookup Time
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Data structures for storing small sets in the bitprobe model
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
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We look at time-space tradeoffs for the static membership problem in the bit-probe model. The problem is to represent a set of size up to n from a universe of size m using a small number of bits so that given an element of the universe, its membership in the set can be determined with as few bit probes to the representation as possible. We show several deterministic upper bounds for the case when the number of bit probes, is small, by explicit constructions, culminating in one that uses o(m) bits of space where membership can be determined with «lg lg n» + 2 adaptive bit probes. We also show two tight lower bounds on space for a restricted two probe adaptive scheme.