### Abstract

Range-summable universal hash functions, also known as range-summable random variables, are binary-valued hash functions which can efficiently hash single values as well as ranges of values from the domain. They have found several applications in the area of data stream processing where they are used to construct sketches - small-space summaries of the input sequence. We present two new constructions of range-summable universal hash functions on n-bit strings, one based on Reed-Muller codes which gives k-universal hashing using O(n ^{log k}) space arid time for point operations and O(n ^{2 1og k}) for range operations, and another based on a new subcode of the second-order Reed-Muller code, which gives 5-universal hashing using O(n) space, O(n log ^{3} n) time for point operations, and O(n ^{3}) time for range operations. We also present a new sketch data structure using the new hash functions which improves several previous results.

Original language | English (US) |
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Pages | 840-849 |

Number of pages | 10 |

State | Published - Jul 1 2005 |

Event | Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms - Vancouver, BC, United States Duration: Jan 23 2005 → Jan 25 2005 |

### Other

Other | Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms |
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Country | United States |

City | Vancouver, BC |

Period | 1/23/05 → 1/25/05 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Improved range-summable random variable construction algorithms*. 840-849. Paper presented at Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Vancouver, BC, United States.

**Improved range-summable random variable construction algorithms.** / Calderbank, A. R.; Gilbert, A.; Levchenko, K.; Muthukrishnan, Shanmugavelayutham; Strauss, M.

Research output: Contribution to conference › Paper

}

TY - CONF

T1 - Improved range-summable random variable construction algorithms

AU - Calderbank, A. R.

AU - Gilbert, A.

AU - Levchenko, K.

AU - Muthukrishnan, Shanmugavelayutham

AU - Strauss, M.

PY - 2005/7/1

Y1 - 2005/7/1

N2 - Range-summable universal hash functions, also known as range-summable random variables, are binary-valued hash functions which can efficiently hash single values as well as ranges of values from the domain. They have found several applications in the area of data stream processing where they are used to construct sketches - small-space summaries of the input sequence. We present two new constructions of range-summable universal hash functions on n-bit strings, one based on Reed-Muller codes which gives k-universal hashing using O(n log k) space arid time for point operations and O(n 2 1og k) for range operations, and another based on a new subcode of the second-order Reed-Muller code, which gives 5-universal hashing using O(n) space, O(n log 3 n) time for point operations, and O(n 3) time for range operations. We also present a new sketch data structure using the new hash functions which improves several previous results.

AB - Range-summable universal hash functions, also known as range-summable random variables, are binary-valued hash functions which can efficiently hash single values as well as ranges of values from the domain. They have found several applications in the area of data stream processing where they are used to construct sketches - small-space summaries of the input sequence. We present two new constructions of range-summable universal hash functions on n-bit strings, one based on Reed-Muller codes which gives k-universal hashing using O(n log k) space arid time for point operations and O(n 2 1og k) for range operations, and another based on a new subcode of the second-order Reed-Muller code, which gives 5-universal hashing using O(n) space, O(n log 3 n) time for point operations, and O(n 3) time for range operations. We also present a new sketch data structure using the new hash functions which improves several previous results.

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M3 - Paper

AN - SCOPUS:20744447741

SP - 840

EP - 849

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