# All-Purpose Hashing

@article{Bender2021AllPurposeH, title={All-Purpose Hashing}, author={Michael A. Bender and Alex Conway and Martin Farach-Colton and William Kuszmaul and Guido Tagliavini}, journal={ArXiv}, year={2021}, volume={abs/2109.04548} }

Despite being one of the oldest data structures in computer science, hash tables continue to be the focus of a great deal of both theoretical and empirical research. A central reason for this is that many of the fundamental properties that one desires from a hash table are difficult to achieve simultaneously; thus many variants offering different trade-offs have been proposed. This paper introduces Iceberg hashing, a hash table that simultaneously offers the strongest known guarantees on a…

## One Citation

On the Optimal Time/Space Tradeoff for Hash Tables

- Computer ScienceArXiv
- 2021

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…

## References

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This paper shows that linear probing, a classical collision resolution strategy for hash tables, can be easily made cache-oblivious but it only achieves tq=1+Θ(α/b) even if a truly random hash function is used, and demonstrates that the block probing algorithm achieves t q=1-1/2Ω(b), thus matching the cache-aware bound.

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This paper presents an almost ideal solution to this problem: a hash function h: U: Uarrow V that, on any set of $n$ inputs, behaves like a truly random function with high probability, can be evaluated in constant time on a RAM and can be stored in $(1+\epsilon)n\log |V| + O(n+\log \log |U|)$ bits.

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This work designs hashing-based indexing schemes for dictionaries and multimaps that achieve worst-case optimal performance for lookups and updates, with a small or negligible probability the data structure will require a rehash operation.

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A new external memory data structure is presented, the BOT, that matches the performance of the IP hash table, while retaining some of the simplicity of the BOAs.

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This paper construction is a two-level variant of cuckoo hashing, augmented with a ``backyard'' that handles a large fraction of the elements, together with a de-amortized perfect hashing scheme for eliminating the dependency on $\boldsymbol{n}$ memory words, and guarantees constant-time operations in the worst case with high probability.

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Earlier analyses of umform hashing are extended here to multlrecord buckets and three different situations are analysed: initial loadmg assuming uniform access frequencies, frequency loading assuming nonuniformAccess frequencies, and the dynamic behavior when msertions and deletions occur.

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A new analysis of the well-known family of multiplicative hash functions, and improved deterministic algorithms for selecting “good” hash functions are presented, for realization of deterministic dictionaries with fast lookups and reasonably fast updates.