## Abstract

We consider the following fundamental problems:

• Constructing k-independent hash functions with a spacetime

tradeoff close to Siegel’s lower bound.

• Constructing representations of unbalanced expander graphs having small size and allowing fast computation of the neighbor function.

It is not hard to show that these problems are intimately connected in the sense that a good solution to one of them leads to a good solution to the other one. In this paper we exploit

this connection to present efficient, recursive constructions of k-independent hash functions (and hence expanders with a small representation). While the previously most efficient construction (Thorup, FOCS 2013) needed time quasipolynomial in Siegel’s lower bound, our time bound is just a logarithmic factor from the lower bound.

• Constructing k-independent hash functions with a spacetime

tradeoff close to Siegel’s lower bound.

• Constructing representations of unbalanced expander graphs having small size and allowing fast computation of the neighbor function.

It is not hard to show that these problems are intimately connected in the sense that a good solution to one of them leads to a good solution to the other one. In this paper we exploit

this connection to present efficient, recursive constructions of k-independent hash functions (and hence expanders with a small representation). While the previously most efficient construction (Thorup, FOCS 2013) needed time quasipolynomial in Siegel’s lower bound, our time bound is just a logarithmic factor from the lower bound.

Original language | English |
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Title of host publication | STOC '15 Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing |

Publisher | Association for Computing Machinery |

Publication date | 2015 |

Pages | 813-820 |

ISBN (Print) | 978-1-4503-3536-2 |

DOIs | |

Publication status | Published - 2015 |

## Keywords

- hashing
- k-independence
- expanders