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Documents authored by Lehmann, Hans-Peter

Artifact
Software
DOI: 10.4230/artifacts.24698
Engineering Minimal k-Perfect Hash Functions

Authors: Stefan Hermann, Sebastian Kirmayer, Hans-Peter Lehmann, and Stefan Walzer

Abstract
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Stefan Hermann, Sebastian Kirmayer, Hans-Peter Lehmann, Stefan Walzer. Engineering Minimal k-Perfect Hash Functions (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{sourceCodekPHF,
   title = {{Engineering Minimal k-Perfect Hash Functions}}, 
   author = {Hermann, Stefan and Kirmayer, Sebastian and Lehmann, Hans-Peter and Walzer, Stefan},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:e6756f018691a80adc68d839fd3617d8f5e2d0b0;origin=https://github.com/stefanfred/engineering-k-perfect-hashing;visit=swh:1:snp:8b568d1c8fe1e13f6ef95d3b2774fc59c259d6b5;anchor=swh:1:rev:2c269037dad34b69a68b56fed38c98656f02c133}{\texttt{swh:1:dir:e6756f018691a80adc68d839fd3617d8f5e2d0b0}} (visited on 2025-10-01)},
   url = {https://github.com/stefanfred/engineering-k-perfect-hashing},
   doi = {10.4230/artifacts.24698},
}
Artifact
Software
DOI: 10.4230/artifacts.23789
ByteHamster/ConsensusRecSplit

Authors: Hans-Peter Lehmann, Peter Sanders, Stefan Walzer, and Jonatan Ziegler

Abstract
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Hans-Peter Lehmann, Peter Sanders, Stefan Walzer, Jonatan Ziegler. ByteHamster/ConsensusRecSplit (Software, Source code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-23789,
   title = {{ByteHamster/ConsensusRecSplit}}, 
   author = {Lehmann, Hans-Peter and Sanders, Peter and Walzer, Stefan and Ziegler, Jonatan},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:eeef738e12bea287eae54a77ce81241587a91767;origin=https://github.com/ByteHamster/ConsensusRecSplit;visit=swh:1:snp:4e488d15839a07248b34bebacd139581927693ba;anchor=swh:1:rev:11deea62b5b507fbac5419ad14c9e2cc0b3ffff8}{\texttt{swh:1:dir:eeef738e12bea287eae54a77ce81241587a91767}} (visited on 2025-10-01)},
   url = {https://github.com/ByteHamster/ConsensusRecSplit},
   doi = {10.4230/artifacts.23789},
}
Artifact
Software
DOI: 10.4230/artifacts.23790
ByteHamster/MPHF-Experiments

Authors: Hans-Peter Lehmann

Abstract
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Hans-Peter Lehmann. ByteHamster/MPHF-Experiments (Software, Comparison with competitors). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-23790,
   title = {{ByteHamster/MPHF-Experiments}}, 
   author = {Lehmann, Hans-Peter},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:7b02eda8ffa5a9d61a086ff2fc34fb0fbdc3eff4;origin=https://github.com/ByteHamster/MPHF-Experiments;visit=swh:1:snp:368a276aa02ccd3cf9f73f14764499ba9a4bff85;anchor=swh:1:rev:d4501ce780b534f0c5a285874558788e49ff3198}{\texttt{swh:1:dir:7b02eda8ffa5a9d61a086ff2fc34fb0fbdc3eff4}} (visited on 2025-10-01)},
   url = {https://github.com/ByteHamster/MPHF-Experiments},
   doi = {10.4230/artifacts.23790},
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.99
Engineering Minimal k-Perfect Hash Functions

Authors: Stefan Hermann, Sebastian Kirmayer, Hans-Peter Lehmann, Peter Sanders, and Stefan Walzer

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

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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Stefan Hermann, Sebastian Kirmayer, Hans-Peter Lehmann, Peter Sanders, and Stefan Walzer. Engineering Minimal k-Perfect Hash Functions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 99:1-99:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hermann_et_al:LIPIcs.ESA.2025.99,
  author =	{Hermann, Stefan and Kirmayer, Sebastian and Lehmann, Hans-Peter and Sanders, Peter and Walzer, Stefan},
  title =	{{Engineering Minimal k-Perfect Hash Functions}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{99:1--99:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.99},
  URN =		{urn:nbn:de:0030-drops-245685},
  doi =		{10.4230/LIPIcs.ESA.2025.99},
  annote =	{Keywords: Compressed Data Structures, Perfect Hashing}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.109
Combined Search and Encoding for Seeds, with an Application to Minimal Perfect Hashing

Authors: Hans-Peter Lehmann, Peter Sanders, Stefan Walzer, and Jonatan Ziegler

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Randomised algorithms often employ methods that can fail and that are retried with independent randomness until they succeed. Randomised data structures therefore often store indices of successful attempts, called seeds. If n such seeds are required (e.g., for independent substructures) the standard approach is to compute for each i ∈ [n] the smallest successful seed S_i and store S = (S_1,…,S_n). The central observation of this paper is that this is not space-optimal. We present a different algorithm that computes a sequence S' = (S_1',…,S_n') of successful seeds such that the entropy of S' undercuts the entropy of S by Ω(n) bits in most cases. To achieve a memory consumption of OPT+εn, the expected number of inspected seeds increases by a factor of 𝒪(1/ε). We demonstrate the usefulness of our findings with a novel construction for minimal perfect hash functions that, for n keys and any ε ∈ [n^{-3/7},1], has space requirement (1+ε)OPT and construction time 𝒪(n/ε). All previous approaches only support ε = ω(1/log n) or have construction times that increase exponentially with 1/ε. Our implementation beats the construction throughput of the state of the art by more than two orders of magnitude for ε ≤ 3%.
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Hans-Peter Lehmann, Peter Sanders, Stefan Walzer, and Jonatan Ziegler. Combined Search and Encoding for Seeds, with an Application to Minimal Perfect Hashing. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 109:1-109:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lehmann_et_al:LIPIcs.ESA.2025.109,
  author =	{Lehmann, Hans-Peter and Sanders, Peter and Walzer, Stefan and Ziegler, Jonatan},
  title =	{{Combined Search and Encoding for Seeds, with an Application to Minimal Perfect Hashing}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{109:1--109:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.109},
  URN =		{urn:nbn:de:0030-drops-245780},
  doi =		{10.4230/LIPIcs.ESA.2025.109},
  annote =	{Keywords: Random Seed, Encoding, Bernoulli Process, Backtracking, Perfect Hashing}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.69
PHOBIC: Perfect Hashing With Optimized Bucket Sizes and Interleaved Coding

Authors: Stefan Hermann, Hans-Peter Lehmann, Giulio Ermanno Pibiri, Peter Sanders, and Stefan Walzer

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
A minimal perfect hash function (or MPHF) maps a set of n keys to [n] : = {1, …, n} without collisions. Such functions find widespread application e.g. in bioinformatics and databases. In this paper we revisit PTHash - a construction technique particularly designed for fast queries. PTHash distributes the input keys into small buckets and, for each bucket, it searches for a hash function seed that places its keys in the output domain without collisions. The collection of all seeds is then stored in a compressed way. Since the first buckets are easier to place, buckets are considered in non-increasing order of size. Additionally, PTHash heuristically produces an imbalanced distribution of bucket sizes by distributing 60% of the keys into 30% of the buckets. Our main contribution is to characterize, up to lower order terms, an optimal choice for the expected bucket sizes, improving construction throughput for space efficient configurations both in theory and practice. Further contributions include a new encoding scheme for seeds that works across partitions of the data structure and a GPU parallelization. Compared to PTHash, PHOBIC is 0.17 bits/key more space efficient for same query time and construction throughput. For a configuration with fast queries, our GPU implementation can construct an MPHF at 2.17 bits/key in 28 ns/key, which can be queried in 37 ns/query on the CPU.
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Stefan Hermann, Hans-Peter Lehmann, Giulio Ermanno Pibiri, Peter Sanders, and Stefan Walzer. PHOBIC: Perfect Hashing With Optimized Bucket Sizes and Interleaved Coding. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 69:1-69:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hermann_et_al:LIPIcs.ESA.2024.69,
  author =	{Hermann, Stefan and Lehmann, Hans-Peter and Pibiri, Giulio Ermanno and Sanders, Peter and Walzer, Stefan},
  title =	{{PHOBIC: Perfect Hashing With Optimized Bucket Sizes and Interleaved Coding}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{69:1--69:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.69},
  URN =		{urn:nbn:de:0030-drops-211405},
  doi =		{10.4230/LIPIcs.ESA.2024.69},
  annote =	{Keywords: Compressed Data Structures, Minimal Perfect Hashing, GPU}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.19
High Performance Construction of RecSplit Based Minimal Perfect Hash Functions

Authors: Dominik Bez, Florian Kurpicz, Hans-Peter Lehmann, and Peter Sanders

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
A minimal perfect hash function (MPHF) bijectively maps a set S of objects to the first |S| integers. It can be used as a building block in databases and data compression. RecSplit [Esposito et al., ALENEX'20] is currently the most space efficient practical minimal perfect hash function. It heavily relies on trying out hash functions in a brute force way. We introduce rotation fitting, a new technique that makes the search more efficient by drastically reducing the number of tried hash functions. Additionally, we greatly improve the construction time of RecSplit by harnessing parallelism on the level of bits, vectors, cores, and GPUs. In combination, the resulting improvements yield speedups up to 239 on an 8-core CPU and up to 5438 using a GPU. The original single-threaded RecSplit implementation needs 1.5 hours to construct an MPHF for 5 Million objects with 1.56 bits per object. On the GPU, we achieve the same space usage in just 5 seconds. Given that the speedups are larger than the increase in energy consumption, our implementation is more energy efficient than the original implementation.
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Dominik Bez, Florian Kurpicz, Hans-Peter Lehmann, and Peter Sanders. High Performance Construction of RecSplit Based Minimal Perfect Hash Functions. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bez_et_al:LIPIcs.ESA.2023.19,
  author =	{Bez, Dominik and Kurpicz, Florian and Lehmann, Hans-Peter and Sanders, Peter},
  title =	{{High Performance Construction of RecSplit Based Minimal Perfect Hash Functions}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.19},
  URN =		{urn:nbn:de:0030-drops-186728},
  doi =		{10.4230/LIPIcs.ESA.2023.19},
  annote =	{Keywords: compressed data structure, parallel perfect hashing, bit parallelism, GPU, SIMD, parallel computing, vector instructions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.46
Learned Monotone Minimal Perfect Hashing

Authors: Paolo Ferragina, Hans-Peter Lehmann, Peter Sanders, and Giorgio Vinciguerra

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
A Monotone Minimal Perfect Hash Function (MMPHF) constructed on a set S of keys is a function that maps each key in S to its rank. On keys not in S, the function returns an arbitrary value. Applications range from databases, search engines, data encryption, to pattern-matching algorithms. In this paper, we describe LeMonHash, a new technique for constructing MMPHFs for integers. The core idea of LeMonHash is surprisingly simple and effective: we learn a monotone mapping from keys to their rank via an error-bounded piecewise linear model (the PGM-index), and then we solve the collisions that might arise among keys mapping to the same rank estimate by associating small integers with them in a retrieval data structure (BuRR). On synthetic random datasets, LeMonHash needs 34% less space than the next larger competitor, while achieving about 16 times faster queries. On real-world datasets, the space usage is very close to or much better than the best competitors, while achieving up to 19 times faster queries than the next larger competitor. As far as the construction of LeMonHash is concerned, we get an improvement by a factor of up to 2, compared to the competitor with the next best space usage. We also investigate the case of keys being variable-length strings, introducing the so-called LeMonHash-VL: it needs space within 13% of the best competitors while achieving up to 3 times faster queries than the next larger competitor.
Cite as

Paolo Ferragina, Hans-Peter Lehmann, Peter Sanders, and Giorgio Vinciguerra. Learned Monotone Minimal Perfect Hashing. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 46:1-46:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ferragina_et_al:LIPIcs.ESA.2023.46,
  author =	{Ferragina, Paolo and Lehmann, Hans-Peter and Sanders, Peter and Vinciguerra, Giorgio},
  title =	{{Learned Monotone Minimal Perfect Hashing}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{46:1--46:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.46},
  URN =		{urn:nbn:de:0030-drops-186990},
  doi =		{10.4230/LIPIcs.ESA.2023.46},
  annote =	{Keywords: compressed data structure, monotone minimal perfect hashing, retrieval}
}
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