Constructing Minimal Perfect Hash Functions Using SAT Technology

Sean Weaver; Marijn Heule

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arXiv · 1911.10099

Constructing Minimal Perfect Hash Functions Using SAT Technology

Sean Weaver·Marijn Heule

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Abstract

Minimal perfect hash functions (MPHFs) are used to provide efficient access to values of large dictionaries (sets of key-value pairs). Discovering new algorithms for building MPHFs is an area of active research, especially from the perspective of storage efficiency. The information-theoretic limit for MPHFs is 1/(ln 2) or roughly 1.44 bits per key. The current best practical algorithms range between 2 and 4 bits per key. In this article, we propose two SAT-based constructions of MPHFs. Our first construction yields MPHFs near the information-theoretic limit. For this construction, current state-of-the-art SAT solvers can handle instances where the dictionaries contain up to 40 elements, thereby outperforming the existing (brute-force) methods. Our second construction uses XOR-SAT filters to realize a practical approach with long-term storage of approximately 1.83 bits per key.

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Sean Weaver, Marijn Heule. 2019-11-22. Constructing Minimal Perfect Hash Functions Using SAT Technology. https://arxiv.org/abs/1911.10099

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