The Multiple-Orientability Thresholds for Random Hypergraphs

Conference paper (2011)

Authors

Nikolaos Fountoulakis University of Birmingham
M. Khosla Max Planck Institut für Informatik
Konstantinos Panagiotou Technische Universität München
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Published Date

2011

Language

English

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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.