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- W4303962008 abstract "For nearly six decades, the central open question in the study of hash tables has been to determine the optimal achievable tradeoff curve between time and space. State-of-the-art hash tables offer the following guarantee: If keys/values are Theta(log n) bits each, then it is possible to achieve constant-time insertions/deletions/queries while wasting only O(loglog n) bits of space per key when compared to the information-theoretic optimum. Even prior to this bound being achieved, the target of O(loglog n) wasted bits per key was known to be a natural end goal, and was proven to be optimal for a number of closely related problems (e.g., stable hashing, dynamic retrieval, and dynamically-resized filters). This paper shows that O(loglog n) wasted bits per key is not the end of the line for hashing. In fact, for any k in [log* n], it is possible to achieve O(k)-time insertions/deletions, O(1)-time queries, and O(log^{(k)} n) wasted bits per key (all with high probability in n). This means that, each time we increase insertion/deletion time by an emph{additive constant}, we reduce the wasted bits per key emph{exponentially}. We further show that this tradeoff curve is the best achievable by any of a large class of hash tables, including any hash table designed using the current framework for making constant-time hash tables succinct." @default.
- W4303962008 created "2022-10-10" @default.
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- W4303962008 date "2021-10-31" @default.
- W4303962008 modified "2023-09-27" @default.
- W4303962008 title "On the Optimal Time/Space Tradeoff for Hash Tables" @default.
- W4303962008 doi "https://doi.org/10.48550/arxiv.2111.00602" @default.
- W4303962008 hasPublicationYear "2021" @default.
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