## Abstract

Let D ⊆ ∑^{n} be a dictionary. We look for efficient data structures and algorithms to solve the following approximate query problem: Given a query u ∈ ∑^{n} list all words v ∈ D that are close to u in Hamming distance. The problem reduces to the following combinatorial problem: Hash the vertices of the n-dimensional hypercube into buckets so that (1) the c-neighborhood of each vertex is mapped into at most k buckets and (2) no bucket is too large. Lower and upper bounds are given for the tradeoff between k and the size of the largest bucket. These results are used to derive bounds for the approximate query problem.

Original language | American English |
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Pages (from-to) | 73-85 |

Number of pages | 13 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - 2002 |

## Keywords

- Approximate query
- Error correcting code
- Hashing
- Isoperimetric inequality