The random walk $d$-ary cuckoo hashing algorithm was defined by Fotakis, Pagh, Sanders, and Spirakis to generalize and improve upon the standard cuckoo hashing algorithm of Pagh and Rodler. Random walk $d$-ary cuckoo hashing has low space overhead, guaranteed fast access, and fast in practice insertion time. In this paper, we give a theoretical insertion time bound for this algorithm. More precisely, for every $d\ge 3$ hashes, let $c_d^*$ be the sharp threshold for the load factor at which a valid assignment of $cm$ objects to a hash table of size $m$ likely exists. We show that for any $d\ge 4$ hashes and load factor $c<c_d^*$, the expectation of the random walk insertion time is $O(1)$, that is, a constant depending only on $d$ and $c$ but not $m$.

翻译：随机游走 d 元布谷鸟哈希算法由 Fotakis、Pagh、Sanders 和 Spirakis 提出，旨在推广并改进 Pagh 和 Rodler 的标准布谷鸟哈希算法。该算法具有较低的空间开销、有保障的快速访问能力以及实际应用中快速的插入时间。本文为该算法提供了插入时间的理论界。更准确地说，对于任意 $d\ge 3$ 个哈希函数，令 $c_d^*$ 为负载因子的尖锐阈值，当负载因子达到该阈值时，将 $cm$ 个对象分配到大小为 $m$ 的哈希表中的有效分配方案很可能存在。我们证明，对于任意 $d\ge 4$ 个哈希函数以及负载因子 $c<c_d^*$，随机游走插入时间的期望为 $O(1)$，即该常数仅依赖于 $d$ 和 $c$，而与 $m$ 无关。