## Uniform Hashing in Constant Time and Linear Space (2003)

Citations: | 12 - 1 self |

### BibTeX

@MISC{Östlin03uniformhashing,

author = {Anna Östlin and Rasmus Pagh},

title = {Uniform Hashing in Constant Time and Linear Space },

year = {2003}

}

### Years of Citing Articles

### OpenURL

### Abstract

Many algorithms and data structures employing hashing have been analyzed under the uniform hashing assumption, i.e., the assumption that hash functions behave like truly random functions. Starting with the discovery of universal hash functions, many researchers have studied to what extent this theoretical ideal can be realized by hash functions that do not take up too much space and can be evaluated quickly. In this paper we present an almost ideal solution to this problem: A hash function that, on any set of n inputs, behaves like a truly random function with high probability, can be evaluated in constant time on a RAM, and can be stored in O(n) words, which is optimal. For many hashing schemes this is the first hash function that makes their uniform hashing analysis come true, with high probability, without incurring overhead in time or space.

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Citation Context ...hat were empirically found to work well in cases where uniform hashing could be shown to work well. The gap between hashing algorithms and their analysis narrowed with the advent of universal hashing =-=[8]-=-. The key insight was that it is often possible to get provable performance guarantees by choosing hash functions at random from a small family of functions (rather than from the family of all functio... |

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Citation Context ...ce parameters (see, e.g., [22, 23]). In addition to the classic hashing schemes, our hash functions provide the first provably efficient implementation of recent load balancing schemes of Azar et al. =-=[4]-=- and by Vöcking and collaborators [6, 26]. Our construction also has an application in cryptography, where it “derandomizes” a construction of Bellare et al. [5] for the most important parameters (see... |

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Citation Context ...). The importance of the family being small is, of course, that a function from the family can be stored succinctly. Following universal hashing, many hash function families have been proposed (e.g., =-=[3, 7, 10, 11, 12, 16, 18, 20, 24]-=-), and their performance analyzed in various settings. One property of the choice of hash function that often suffices to give performance guarantees is that it maps each set of k elements in U to uni... |

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Citation Context ...). The importance of the family being small is, of course, that a function from the family can be stored succinctly. Following universal hashing, many hash function families have been proposed (e.g., =-=[3, 7, 10, 11, 12, 16, 18, 20, 24]-=-), and their performance analyzed in various settings. One property of the choice of hash function that often suffices to give performance guarantees is that it maps each set of k elements in U to uni... |

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Citation Context ... load balancing schemes of Azar et al. [4] and by Vöcking and collaborators [6, 26]. Our construction also has an application in cryptography, where it “derandomizes” a construction of Bellare et al. =-=[5]-=- for the most important parameters (see discussion in Section 3.1.1). 1.4 Overview of the paper The organization of the paper is as follows. In section 2 we provide the background information necessar... |

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Citation Context |