AI 中文总结
研究布谷鸟哈希的快速插入问题，提出新插入过程，能将哈希表填充到接近最优阈值的负载因子，有poly(ε^-1)插入时间界和强摊销保证，传统算法无法匹配，且查询算法能大概率猜出键所在桶，提升查询效率。
AI 中文摘要
布谷鸟哈希是一种实用高效的哈希表方案，每个对象u存储在两个容量为ℓ的桶h1(u)、h2(u)之一。对于任意桶大小ℓ，存在阈值ε*(ℓ)=(2/e)^ℓ poly(ℓ)，能以低错误概率将哈希表填充到小于1 - ε*的任意负载因子。查询和删除只需检查两个桶。我们给出了新的插入过程，对于任意δ∈[.99^ℓ,1]，算法能将哈希表填充到负载因子1 - ε = 1 - (1 + δ)(ε*)，每次插入期望运行时间为O(δ^-1(ε*)^-1)，这是首个poly(ε^-1)插入时间界，且算法有很强的摊销保证，传统随机游走算法无法匹配。此外，插入协议还使查询算法能以1 - o(1)的概率正确猜出键u所在桶，正查询能在1 + o(1)次期望桶访问中完成。
英文摘要
Bucketized cuckoo hashing is a practically efficient hash table scheme in which each object $u$ is stored in one of two buckets $h_1(u), h_2(u)$ of capacity $\ell$. For any bucket size $\ell\in\mb{N}$, there is a threshold $ε^*(\ell)=(2/e)^\ell\mathrm{poly}(\ell)$ for which there exists a way to fill the hash table to any load factor less than $1-ε^*$ with low probability of an error. Queries and deletions only need to check two buckets to find whether an object exists. Our contribution is to give a new insertion procedure for bucketized cuckoo hashing. For any $δ\in[.99^\ell,1]$, our algorithm can fill the hash table to load factor $1-ε=1-(1+δ)(ε^*)$ with an expected run time of $O(δ^{-1}(ε^*)^{-1})$ per insertion. This gives the first $\mathrm{poly}(ε^{-1})$ insertion time bound, and the first $f(ε^{-1})$ time bound for load factors that are very close to the optimal threshold. Additionally, our algorithm (which can be viewed as a variation of the classic random-walk algorithm) comes with a very strong amortized guarantee: it performs $O(1)$ amortized expected evictions per insertion. Furthermore, we show that the traditional random-walk algorithm cannot match this guarantee. Finally, our insertion protocol also comes with the feature that, for any key $u$ in the hash table, the query algorithm can \emph{guess} which of the two bins $h_1(u), h_2(u)$ the key $u$ is in with probability $1 - o(1)$ of being correct. Thus positive queries can complete in $1 + o(1)$ expected bin accesses.
CommentsFOCS 2026
