经典开放寻址的紧界
Tight Bounds for Classical Open Addressing
AI总结：
本研究提出rainbow hashing经典开放寻址哈希表，证明其时间-负载因子权衡最优，且扩展动态调整大小无额外时间成本，解决了此前三类操作同时达o(ε⁻¹)时间界的开放问题。
摘要：
我们提出了一种名为rainbow hashing（彩虹哈希）的经典开放寻址哈希表，该哈希表支持最高$1 - \varepsilon$的负载因子，同时具备$O(1)$的期望查询时间，以及$O(\log \log \varepsilon^{-1})$的期望插入和删除时间。我们进一步证明该权衡曲线是最优的：任何支持负载因子$1 - \varepsilon$的经典开放寻址哈希表，每次操作的期望时间都必须为$\Omega(\log \log \varepsilon^{-1})$。最后，我们将rainbow hashing扩展到哈希表随时间动态调整大小的场景。令人意外的是，添加动态调整大小功能不会产生任何时间成本——即使始终维持不低于$1 - \varepsilon$的负载因子，我们仍可支持$O(1)$的查询和$O(\log \log \varepsilon^{-1})$的更新。在我们的工作之前，同时为插入、删除和查询操作实现任何形如$o(\varepsilon^{-1})$的时间界仍是一个开放问题。
英文摘要：
We introduce a classical open-addressed hash table, called rainbow hashing, that supports a load factor of up to $1 - \varepsilon$, while also supporting $O(1)$ expected-time queries, and $O(\log \log \varepsilon^{-1})$ expected-time insertions and deletions. We further prove that this tradeoff curve is optimal: any classical open-addressed hash table that supports load factor $1 - \varepsilon$ must incur $Ω(\log \log \varepsilon^{-1})$ expected time per operation. Finally, we extend rainbow hashing to the setting where the hash table is dynamically resized over time. Surprisingly, the addition of dynamic resizing does not come at any time cost -- even while maintaining a load factor of $\ge 1 - \varepsilon$ at all times, we can support $O(1)$ queries and $O(\log \log \varepsilon^{-1})$ updates. Prior to our work, achieving any time bounds of the form $o(\varepsilon^{-1})$ for all of insertions, deletions, and queries simultaneously remained an open question.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
