2026-10-23T02:36:40Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24568 2025-12-17T09:34:25Z ddc:004 open_access

Engineering Minimal k-Perfect Hash Functions Hermann, Stefan Kirmayer, Sebastian Lehmann, Hans-Peter Sanders, Peter Walzer, Stefan Compressed Data Structures Perfect Hashing 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Stefan Hermann and Sebastian Kirmayer and Hans-Peter Lehmann and Peter Sanders and Stefan Walzer 2025 Is Part Of LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2025.99 urn:nbn:de:0030-drops-245685 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.99 eng https://creativecommons.org/licenses/by/4.0/legalcode