Cache-Oblivious Dictionaries and Multimaps with Negligible Failure Probability

A dictionary (or map) is a key-value store that requires all keys be unique, and a multimap is a key-value store that allows for multiple values to be associated with the same key. We design hashing-based indexing schemes for dictionaries and multimaps that achieve worst-case optimal performance for lookups and updates, with minimal space overhead and sub-polynomial probability that the data structure will require a rehash operation. Our dictionary structure is designed for the Random Access Machine (RAM) model, while our multimap implementation is designed for the cache-oblivious external memory (I/O) model. The failure probabilities for our structures are sub-polynomial, which can be useful in cryptographic or data-intensive applications.