History of Cuckoo hashing thresholds of random $k$-uniform hypergraphs

 Title: Cuckoo hashing thresholds of random $k$-uniform hypergraphs-Definition: 'An $\ell$-orientable hypergraph is one whose edges can be assigned to-  incident vertices so that no vertex receives more than $\ell$ edges. In the random-  $k$-uniform hypergraph CITE{WikiHypergraph} with $n$ vertices and $m=\lfloor cn\rfloor$-  edges, $c^*_{k,\ell}$ is the threshold density: as $n\to\infty$, the probability-  of $\ell$-orientability tends to $1$ for $c<c^*_{k,\ell}$ and to $0$ for $c>c^*_{k,\ell}$-  CITE{FKP}.'+Definition: An $\ell$-orientation assigns each edge to one of its vertices, with at+  most $\ell$ edges at any vertex. In the random $k$-uniform hypergraph CITE{WikiHypergraph}+  with $n$ vertices and $\lfloor cn\rfloor$ edges, $c^*_{k,\ell}$ is the high-probability+  threshold for $\ell$-orientability CITE{FKP}. Keywords: orientability threshold, blocked cuckoo hashing, multiple-choice hashing,   balanced allocation

     constraints: $\ell\geq1$ Comments:-  comment-orientation: In hashing language, edges are keys and vertices are buckets,-    so $c^*_{k,\ell}$ is the threshold for the number of keys per bucket in offline-    cuckoo hashing CITE{WikiCuckoo} with $k$ choices and bucket capacity $\ell$ CITE{DGMMPR}.-    The load factor, keys per slot, is $c^*_{k,\ell}/\ell$.+  comment-orientation: The high-probability threshold means that, as $n\to\infty$,+    $\ell$-orientability has probability tending to $1$ for $c<c^*_{k,\ell}$ and to+    $0$ for $c>c^*_{k,\ell}$. In hashing language, edges are keys and vertices are+    buckets, so $c^*_{k,\ell}$ is the threshold for the number of keys per bucket+    in offline cuckoo hashing CITE{WikiCuckoo} with $k$ choices and bucket capacity+    $\ell$ CITE{DGMMPR}. The load factor, keys per slot, is $c^*_{k,\ell}/\ell$.   comment-conventions: 'The density is $c=m/n$, so the average hypergraph degree is     $kc$. Dietzfelbinger, Goerdt, Mitzenmacher, Montanari, Pagh and Rink tabulate