# Storing a sparse table with O(1) worst case access time

@article{Fredman1982StoringAS, title={Storing a sparse table with O(1) worst case access time}, author={Michael L. Fredman and John Komlos and Endre Szemer{\'e}di}, journal={23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)}, year={1982}, pages={165-169} }

We describe a data structure for representing a set of n items from a universe of m items, which uses space n+o(n) and accommodates membership queries in constant time. Both the data structure and the query algorithm are easy to implement.

## 780 Citations

Simple Fast Parallel Hashing

- Computer Science, MathematicsICALP
- 1994

This work shows how to construct a hash table for any given set of n keys in O(lg lg n) parallel time with high probability, using n processors on a weak version of a crcw pram.

Storing a dynamic sparse table

- Computer Science27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
- 1986

We present a family of data structures that can process a sequence of insert, delete, and lookup instructions such that each lookup and deletion is done in constant worst-case time and each insertion…

Membership in Constant Time and Minimum Space

- Computer ScienceESA
- 1994

We investigate the problem of storing a subset of the elements of a bounded universe so that searches can be performed in constant time and the space used is within a constant factor of the minimum…

Approximate Dictionary Queries

- Computer ScienceCPM
- 1996

This work considers the problem of answering d-queries, given a binary query string α of length m, and a d-query is to report if there exists a string in the set within Hamming distance d of α.

LOW REDUNDANCY IN STATIC DICTIONARIES WITH CONSTANT QUERY TIME

- Computer Science
- 2001

It is shown that on a unit cost RAM with word size Θ(log |U |), a static dictionary for n-element sets with constant worst case query time can be obtained using B+O(log log |U|)+o(n) bits of storage, where B e is the minimum number of bits needed to represent all nelement subsets of U.

Applications of Range Query Theory to Relational Data Base Join and Selection Operations

- Computer ScienceJ. Comput. Syst. Sci.
- 1996

Range query theory is applied to develop join algorithms that run inO(IlogdI+U) time, where I and U are the sizes of the input and output anddis usually a small constant, which leads to the development of very fast indices supportingO(PolylogN) selection operations.

Low Redundancy in Static Dictionaries with O(1) Worst Case Lookup Time

- Computer ScienceICALP
- 1999

This work shows that for n-element subsets, constant worst case query time can be obtained using B + O(log log |U|) + o(n) bits of storage, where B = ⌈log2 (n|U|⌉ is the minimum number of bits needed to represent all such subsets.

Dynamic perfect hashing: upper and lower bounds

- Computer Science[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
- 1988

An Omega (log n) lower bound is proved for the amortized worst-case time complexity of any deterministic algorithm in a class of algorithms encompassing realistic hashing-based schemes.

Bounded Ordered Dictionaries in O(log log N) Time and O(n) Space

- Mathematics, Computer ScienceInf. Process. Lett.
- 1990

## References

SHOWING 1-6 OF 6 REFERENCES

Should tables be sorted?

- Computer Science19th Annual Symposium on Foundations of Computer Science (sfcs 1978)
- 1978

It is shown that, in a rather general model including al1 the commonly-used schemes, $\lceil $ lg(n+l) $\rceil$ probes to the table are needed in the worst case, provided the key space is sufficiently large.

Storing a sparse table

- Computer ScienceCACM
- 1979

This work proposes a good worst-case method for storing a static table of n entries, each an integer between 0 and N - 1, and analysis shows why a simpler algorithm used for compressing LR parsing tables works so well.

Reciprocal hashing: a method for generating minimal perfect hashing functions

- Computer Science, MathematicsCACM
- 1981

A method is presented for building minimal perfect hash functions, i.e., functions which allow single probe retrieval from minimally sized tables of identifier sets. A proof of existence for minimal…

Perfect hashing functions: a single probe retrieving method for static sets

- Computer ScienceCACM
- 1977

A refinement of hashing which allows retrieval of an item in a static table with a single probe is considered, and a rough comparison with ordinary hashing is given which shows that this method can be used conveniently in several practical applications.

RECEIVED DECEMBER REVISED JANUARY

- RECEIVED DECEMBER REVISED JANUARY
- 1982