### Abstract

A mechanism is provided for constructing log-n--wise-independent hash functions that can be evaluated in O(1) time. A probabilistic argument shows that for fixed ε < 1, a table of n^{ε} random words can be accessed by a small O(1)-time program to compute one important family of hash functions. An explicit algorithm for such a family, which achieves comparable performance for all practical purposes, is also given. A lower bound shows that such a program must take Ω(k/ε) time, and a probabilistic argument shows that programs can run in O(k^{2}/ε^{2}) time. An immediate consequence of these constructions is that double hashing using these universal functions has (constant factor) optimal performance in time, for suitably moderate loads. Another consequence is that a T-time PRAM (parallel random-access machine) algorithm for n log n processors (and n^{k} memory) can be emulated on an n-processor machine interconnected by an n × log n Omega network with a multiplicative penalty for total work that, with high probability, is only O(1).

Original language | English (US) |
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Title of host publication | Annual Symposium on Foundations of Computer Science (Proceedings) |

Publisher | Publ by IEEE |

Pages | 20-25 |

Number of pages | 6 |

ISBN (Print) | 0818619821 |

State | Published - Nov 1989 |

Event | 30th Annual Symposium on Foundations of Computer Science - Research Triangle Park, NC, USA Duration: Oct 30 1989 → Nov 1 1989 |

### Other

Other | 30th Annual Symposium on Foundations of Computer Science |
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City | Research Triangle Park, NC, USA |

Period | 10/30/89 → 11/1/89 |

### Fingerprint

### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Annual Symposium on Foundations of Computer Science (Proceedings)*(pp. 20-25). Publ by IEEE.

**On universal classes of fast high performance hash functions, their time-space tradeoff, and their applications.** / Siegel, Alan.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Annual Symposium on Foundations of Computer Science (Proceedings).*Publ by IEEE, pp. 20-25, 30th Annual Symposium on Foundations of Computer Science, Research Triangle Park, NC, USA, 10/30/89.

}

TY - GEN

T1 - On universal classes of fast high performance hash functions, their time-space tradeoff, and their applications

AU - Siegel, Alan

PY - 1989/11

Y1 - 1989/11

N2 - A mechanism is provided for constructing log-n--wise-independent hash functions that can be evaluated in O(1) time. A probabilistic argument shows that for fixed ε < 1, a table of nε random words can be accessed by a small O(1)-time program to compute one important family of hash functions. An explicit algorithm for such a family, which achieves comparable performance for all practical purposes, is also given. A lower bound shows that such a program must take Ω(k/ε) time, and a probabilistic argument shows that programs can run in O(k2/ε2) time. An immediate consequence of these constructions is that double hashing using these universal functions has (constant factor) optimal performance in time, for suitably moderate loads. Another consequence is that a T-time PRAM (parallel random-access machine) algorithm for n log n processors (and nk memory) can be emulated on an n-processor machine interconnected by an n × log n Omega network with a multiplicative penalty for total work that, with high probability, is only O(1).

AB - A mechanism is provided for constructing log-n--wise-independent hash functions that can be evaluated in O(1) time. A probabilistic argument shows that for fixed ε < 1, a table of nε random words can be accessed by a small O(1)-time program to compute one important family of hash functions. An explicit algorithm for such a family, which achieves comparable performance for all practical purposes, is also given. A lower bound shows that such a program must take Ω(k/ε) time, and a probabilistic argument shows that programs can run in O(k2/ε2) time. An immediate consequence of these constructions is that double hashing using these universal functions has (constant factor) optimal performance in time, for suitably moderate loads. Another consequence is that a T-time PRAM (parallel random-access machine) algorithm for n log n processors (and nk memory) can be emulated on an n-processor machine interconnected by an n × log n Omega network with a multiplicative penalty for total work that, with high probability, is only O(1).

UR - http://www.scopus.com/inward/record.url?scp=0024768554&partnerID=8YFLogxK

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M3 - Conference contribution

AN - SCOPUS:0024768554

SN - 0818619821

SP - 20

EP - 25

BT - Annual Symposium on Foundations of Computer Science (Proceedings)

PB - Publ by IEEE

ER -