Not all keys can be hashed in constant time

A multitude of models and algorithms for hashing have been suggested and analyzed. However, almost all of them are specific in their assumptions and results. We present a simple new model that captures many natural (sequential and parallel) hashing algorithms. In a game against nature, the algorithm and coin-tosses cause the evolution of a random tree, whose size corresponds to space (hash table size), and two notions of depth correspond respectively to the largest probe sequences for insertion (parallel insertion time) and search of a key.

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