A k-uniform hypergraph H=(V,E) is called β-orientable, if there
is an assignment of each edge eβE to one of its vertices vβe such
that no vertex is assigned more than β edges. Let Hn,m,kβ 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 β-orientability of Hn,m,kβ for all kβ₯3 and
ββ₯2, i.e., we determine a critical quantity ck,βββ such that
with probability 1βo(1) the graph Hn,cn,kβ has an β-orientation if
cck,βββ.
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.Comment: An extended abstract appeared in the proceedings of SODA 201