Engineering Minimal k-Perfect Hash Functions

Stefan Hermann; Sebastian Kirmayer; Hans-Peter Lehmann; Peter Sanders; Stefan Walzer

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arXiv · 2504.20001

Engineering Minimal k-Perfect Hash Functions

Stefan Hermann·Sebastian Kirmayer·Hans-Peter Lehmann·Peter Sanders·Stefan Walzer

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Abstract

Given a set S of n keys, a k-perfect hash function (kPHF) is a data structure that maps the keys to the first m integers, where each output integer can be hit by at most k input keys. When m=n/k, the resulting function is called a minimal k-perfect hash function (MkPHF). Applications of kPHFs can be found in external memory data structures or to create efficient 1-perfect hash functions, which in turn have a wide range of applications from databases to bioinformatics. Several papers from the 1980s look at external memory data structures with small internal memory indexes. However, actual k-perfect hash functions are surprisingly rare, and the area has not seen a lot of research recently. At the same time, recent research in 1-perfect hashing shows that there is a lack of efficient kPHFs. In this paper, we revive the area of k-perfect hashing, presenting four new constructions. Our implementations simultaneously dominate older approaches in space consumption, construction time, and query time. We see this paper as a possible starting point of an active line of research, similar to the area of 1-perfect hashing.

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BibTeX RIS

Stefan Hermann, Sebastian Kirmayer, Hans-Peter Lehmann, Peter Sanders, Stefan Walzer. 2025-04-28. Engineering Minimal k-Perfect Hash Functions. https://arxiv.org/abs/2504.20001

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