On the cell probe complexity of membership and perfect hashing

Authors:
Rasmus Pagh
Affiliations:
BRICS, Department of Computer Science, Ny Munkegade Bldg. 540, 8000 Aarhus C, University of Aarhus, Denmark
Venue:
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Year:
2001

Citing 10
Cited 12

Storing a Sparse Table with 0(1) Worst Case Access Time

Journal of the ACM (JACM)
Uniform hashing is optimal

Journal of the ACM (JACM)
The spatial complexity of oblivious k-probe Hash functions

SIAM Journal on Computing
Chernoff-Hoeffding bounds for applications with limited independence

SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Should Tables Be Sorted?

Journal of the ACM (JACM)
Balanced Allocations

SIAM Journal on Computing
Are bitvectors optimal?

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
Randomized Allocation Processes

FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Perceptrons: An Introduction to Computational Geometry

Perceptrons: An Introduction to Computational Geometry

One-Probe Search

ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Cuckoo Hashing

ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Explicit Deterministic Constructions for Membership in the Bitprobe Model

ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Lossy Dictionaries

ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Almost random graphs with simple hash functions

Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Cuckoo hashing

Journal of Algorithms
On risks of using cuckoo hashing with simple universal hash classes

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Weaknesses of Cuckoo Hashing with a Simple Universal Hash Class: The Case of Large Universes

SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Bit-probe lower bounds for succinct data structures

Proceedings of the forty-first annual ACM symposium on Theory of computing
The limits of buffering: a tight lower bound for dynamic membership in the external memory model

Proceedings of the forty-second ACM symposium on Theory of computing
On the cell probe complexity of dynamic membership

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The Complexity of Distributions

SIAM Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study two fundamental static data structure problems, membership and perfect hashing, in Yao's cell probe model. The first space and bit probe optimal worst case upper bound is given for the membership problem. We also give a new efficient membership scheme where the query algorithm makes just one adaptive choice, and probes a total of three words. A lower bound shows that two word probes generally do not suffice. For minimal perfect hashing we show a tight bit probe lower bound, and give a simple scheme achieving this performance, making just one adaptive choice. Linear range perfect hashing is shown to be implementable with the same number of bit probes, of which just one is adaptive. In contrast, we establish that for sufficiently sparse sets, non-adaptive perfect hashing needs exponentially more bit probes. This is the first such separation of adaptivity and non-adaptivity.