Consistent hashing is a technique for distributing data across a network of nodes in a way that minimizes reorganization when nodes join or leave the network. It is extensively applied in modern distributed systems as a fundamental mechanism for routing and data placement. Similarly, distributed storage systems rely on consistent hashing for scalable and fault-tolerant data partitioning. This paper introduces BinomialHash, a consistent hashing algorithm that executes in constant time and requires minimal memory. We provide a detailed explanation of the algorithm, present a pseudo-code implementation, and formally establish its strong theoretical guarantees. Finally, we compare its performance against state-of-the-art constant-time consistent hashing algorithms, demonstrating that our solution is both highly competitive and effective, while also validating the theoretical boundaries.

翻译：一致性哈希是一种在节点网络中分配数据的技术，其目标是在节点加入或离开网络时最小化数据重组。作为路由和数据放置的基础机制，该技术在现代分布式系统中得到了广泛应用。同样，分布式存储系统也依赖一致性哈希来实现可扩展且容错的数据分区。本文介绍了二项哈希，一种在常数时间内执行且仅需最小内存的一致性哈希算法。我们详细阐述了该算法，给出了伪代码实现，并正式建立了其坚实的理论保证。最后，我们将其性能与最先进的常数时间一致性哈希算法进行了比较，结果表明我们的解决方案不仅极具竞争力且高效，同时也验证了理论边界。