Tootfinder

PHOBIC: Perfect Hashing with Optimized Bucket Sizes and Interleaved Coding
Stefan Hermann, Hans-Peter Lehmann, Giulio Ermanno Pibiri, Peter Sanders, Stefan Walzer
https://arxiv.org/abs/2404.18497 https://arxiv.org/pdf/2404.18497
arXiv:2404.18497v1 Announce Type: new
Abstract: A minimal perfect hash function (MPHF) maps a set of n keys to {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 distribution of expected bucket sizes. We arrive at a simple, closed form solution which improves construction throughput for space efficient configurations in practice. Our second contribution is a novel encoding scheme for the seeds. We split the keys into partitions. Within each partition, we run the bucket distribution and search step. We then store the seeds in an interleaved way by consecutively placing the seeds for the i-th buckets from all partitions. The seeds for the i-th bucket of each partition follow the same statistical distribution. This allows us to tune a compressor for each bucket. Hence, we call our technique PHOBIC - Perfect Hashing with Optimized Bucket sizes and Interleaved Coding. Compared to PTHash, PHOBIC is 0.17 bits/key more space efficient for same query time and construction throughput. We also contribute a GPU implementation to further accelerate MPHF construction. For a configuration with fast queries, PHOBIC-GPU can construct a perfect hash function at 2.17 bits/key in 28 ns per key, which can be queried in 37 ns on the CPU.

This https://arxiv.org/abs/2204.01665 has been replaced.
link: https://scholar.google.com/scholar?q=a

Linear Hashing with $\ell_\infty$ guarantees and two-sided Kakeya bounds
We show that a randomly chosen linear map over a finite field gives a good hash function in the $\ell_\infty$ sense. More concretely, consider a set $S \subset \mathbb{F}_q^n$ and a randomly chosen linear map $L : \mathbb{F}_q^n \to \mathbb{F}_q^t$ with $q^t$ taken to be sufficiently smaller than $ |S|$. Let $U_S$ denote a random variable distributed uniformly on $S$. Our main theorem shows that, with high probability over the choice of $L$, the random variable $L(U_S)$ is close to un…

This https://arxiv.org/abs/2403.07760 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Simplified Tight Bounds for Monotone Minimal Perfect Hashing
Given an increasing sequence of integers $x_1,\ldots,x_n$ from a universe $\{0,\ldots,u-1\}$, the monotone minimal perfect hash function (MMPHF) for this sequence is a data structure that answers the following rank queries: $rank(x) = i$ if $x = x_i$, for $i\in \{1,\ldots,n\}$, and $rank(x)$ is arbitrary otherwise. Assadi, Farach-Colton, and Kuszmaul recently presented at SODA'23 a proof of the lower bound $Ω(n \min\{\log\log\log u, \log n\})$ for the bits of space required by MMPHF, provided …

Simplified Tight Bounds for Monotone Minimal Perfect Hashing
Dmitry Kosolobov
https://arxiv.org/abs/2403.07760 https://arxiv.org/pdf/…

Simplified Tight Bounds for Monotone Minimal Perfect Hashing
Given an increasing sequence of integers $x_1,\ldots,x_n$ from a universe $\{0,\ldots,u-1\}$, the monotone minimal perfect hash function (MMPHF) for this sequence is a data structure that answers the following rank queries: $rank(x) = i$ if $x = x_i$, for $i\in \{1,\ldots,n\}$, and $rank(x)$ is arbitrary otherwise. Assadi, Farach-Colton, and Kuszmaul recently presented at SODA'23 a proof of the lower bound $Ω(n \min\{\log\log\log u, \log n\})$ for the bits of space required by MMPHF, provided …