Given a set $S$ of $n$ keys, a perfect hash function for $S$ maps the keys in $S$ to the first $m \geq n$ integers without collisions. It may return an arbitrary result for any key not in $S$ and is called minimal if $m = n$. The most important parameters are its space consumption, construction time, and query time. Years of research now enable modern perfect hash functions to be extremely fast to query, very space-efficient, and scale to billions of keys. Different approaches give different trade-offs between these aspects. For example, the smallest constructions get within 0.1% of the space lower bound of $\log_2(e)$ bits per key. Others are particularly fast to query, requiring only one memory access. Perfect hashing has many applications, for example to avoid collision resolution in static hash tables, and is used in databases, bioinformatics, and stringology. Since the last comprehensive survey in 1997, significant progress has been made. This survey covers the latest developments and provides a starting point for getting familiar with the topic. Additionally, our extensive experimental evaluation can serve as a guide to select a perfect hash function for use in applications.

翻译：给定一个包含 $n$ 个键的集合 $S$，完美哈希函数将 $S$ 中的键无碰撞地映射到前 $m \geq n$ 个整数。对于不在 $S$ 中的任意键，它可能返回任意结果；若 $m = n$，则称为最小完美哈希函数。其最重要的参数包括空间占用、构建时间和查询时间。经过多年的研究，现代完美哈希函数已能在查询时极为快速、空间效率极高，并可扩展至数十亿键的规模。不同的方法在这些方面提供了不同的权衡。例如，最小的构造方案可将空间占用控制在每键 $\log_2(e)$ 比特的空间下界的 0.1% 以内。另一些方案则特别注重查询速度，仅需一次内存访问。完美哈希具有广泛的应用，例如用于避免静态哈希表中的碰撞处理，并在数据库、生物信息学和字符串学等领域得到使用。自 1997 年上一次全面综述以来，该领域已取得显著进展。本综述涵盖了最新发展，为熟悉该主题提供了一个起点。此外，我们广泛的实验评估可作为选择适用于具体应用的完美哈希函数的指南。