BinomialHash: A Constant Time, Minimal Memory Consistent Hash Algorithm

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.