Mphf on CuriousCoding

Overview of static data structures

Wed, 17 Dec 2025 00:00:00 +0100

Table of Contents

1 Classification of static data structures
2 Space lower bounds and practical approaches
- 2.1 Rank
- 2.2 Rank + Select
- 2.3 Minimal perfect hash function (MPHF)
- 2.4 TODO Monotone MPHF
- 2.5 TODO Order-preserving MPHF
- 2.6 Static retrieval: Static function with static values
- 2.7 Updatable retrieval: Static function with mutable values
- 2.8 Static set (membership)
- 2.9 Static ordered set
- 2.10 Static dictionary: static keys and values
- 2.11 Updatable dictionary with mutable values
- 2.12 TODO Dynamic dictionary with mutable keys and values
- 2.13 TODO Static filter
- 2.14 TODO Ordered static/updatable/dynamic dictionary?
3 Summary table

\[ \newcommand{\K}{\mathbb K} \newcommand{\V}{\mathbb V} \newcommand{\c}[1]{\mathbf{\mathsf{#1}}} \]

PtrHash

Sun, 20 Jul 2025 00:00:00 +0200

Minimal Perfect Hash Functions Link to heading

A set of \(n\) keys Link to heading

A hash function Link to heading

A hash function: collisions! Link to heading

A hash function: injective / perfect Link to heading

A hash function: bijective / minimal & perfect Link to heading

Problem statement Link to heading

Given a set of \(n\) keys \(K\subseteq \mathbb K\), build a function \(h\) satisfying

Thoughts on Consensus MPHF and tiny pointers

Wed, 12 Feb 2025 00:00:00 +0100

Table of Contents

1 Consensus
- 1.1 Consensus-RecSplit
2 IDEA: Consensus-PtrHash
3 Tiny pointers and optimal open addressing hash tables

These are some thoughts on the Consensus-based MPHF presented in Lehmann et al. (2025), and how this could be applied to PtrHash:

Lehmann, Hans-Peter, Peter Sanders, Stefan Walzer, and Jonatan Ziegler. 2025. “Combined Search and Encoding for Seeds, with an Application to Minimal Perfect Hashing.” Arxiv. https://doi.org/10.48550/ARXIV.2502.05613.

Below are also some thoughts on the papers on tiny pointers, used to achieve hash tables with load factors very close to 1: Bender et al. (2021), Farach-Colton, Krapivin, and Kuszmaul (2024).

PtrHash: Minimal Perfect Hashing at RAM Throughput

Mon, 03 Feb 2025 00:00:00 +0100

Table of Contents

Abstract
1 Introduction
2 Related work
3 PtrHash
- 3.1 Overview
- 3.2 Construction
- 3.3 Bucket Assignment Functions
- 3.4 Remapping using CacheLineEF
4 Results
- 4.1 Construction
  - 4.1.1 Bucket Functions
  - 4.1.2 Tuning Parameters for Construction
  - 4.1.3 Remap
- 4.2 Comparison to Other Methods
5 Conclusions and Future Work
Appendix A: Query Throughput
Appendix B: Sharding
- Evaluation

This is the online version of my SEA 2025 paper on PtrHash (DOI, PDF). The original development-log can be found here.

Notes on SsHash

Mon, 15 Jan 2024 00:00:00 +0100

Table of Contents

Paper summary
Remarks
Ideas

\[\newcommand{\S}{\mathcal{S}}\]

Paper summary Link to heading

Intro Link to heading

SsHash (Pibiri 2022) is a datastructure for indexing kmers. Given a set of kmers \(\S\), it supports two operations:

\(Lookup(g)\): return the unique id \(i\in [|\S|]\) of the kmer \(g\).
\(Access(i)\): return the kmer corresponding to id \(i\).

It also supports streaming queries, looking up all kmers from a longer string consecutively, by expoiting the overlap between them.

PtrHash: Notes on adapting PTHash in Rust

Thu, 21 Sep 2023 00:00:00 +0200

Table of Contents

Questions and remarks on PTHash paper
Ideas for improvement
Implementation log
PtrHash, part 2
- Phobic
  - TODO for PtrHash

\[ %\newcommand{\mm}{\,\%\,} \newcommand{\mm}{\bmod} \newcommand{\lxor}{\oplus} \newcommand{\K}{\mathcal K} \]

BBHash: some ideas

Mon, 04 Sep 2023 00:00:00 +0200

Table of Contents

Possible speedup?

BBHash Limasset et al. (2017) uses multiple layers to create a minimal perfect hashing functions (MPHF), that hashes some input set into \([n]\).

(See also my note on PTHash (Pibiri and Trani 2021).)

Simply said, it maps the \(n\) elements into \([\gamma \cdot n]\) using hashing function \(h_0\). The \(k_0\) elements that have collisions are mapped into \([\gamma \cdot k_0]\) using \(h_1\). Then, the \(k_1\) elements with collisions are mapped into \([\gamma \cdot k_1]\), and so on.