## Abstract

A k-uniform hypergraph H = (V, E) is called ℓ-orientable, if there is an assignment of each edge e ∊ E to one of its vertices v G e such that no vertex is assigned more than ℓ edges. Let Hn,m,k be a hypergraph, drawn uniformly at random from the set of all k-uniform hypergraphs with n vertices and m edges. In this paper we establish the threshold for the ℓ-orientability of Hn,m,k for all k ≥ 3 and ℓ > 1, i.e., we determine a critical quantity c*k,ℓ such that with probability 1 − o(1) the graph Hn,cn,k has an ℓ-orientation if c*k,ℓ, but fails doing so if c > c*k,ℓ.

Our result has various applications including sharp load thresholds for cuckoo hashing, load balancing with guaranteed maximum load, and massive parallel access to hard disk arrays.

Our result has various applications including sharp load thresholds for cuckoo hashing, load balancing with guaranteed maximum load, and massive parallel access to hard disk arrays.

Original language | English |
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Title of host publication | Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms (SODA'11 |

Editors | Dana Randall |

Pages | 1222-1236 |

Volume | 25 |

Edition | 6 |

Publication status | Published - 2011 |

Externally published | Yes |

Event | ACM-SIAM symposium on Discrete algorithms - Duration: 23 Jan 2011 → 25 Jan 2011 Conference number: 22 |

### Publication series

Name | Combinatorics, Probability and Computing |
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### Conference

Conference | ACM-SIAM symposium on Discrete algorithms |
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Abbreviated title | SODA'11 |

Period | 23/01/11 → 25/01/11 |