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A function $f : U \to \{0,\ldots,n-1\}$ is a minimal perfect hash functionfor a set $S \subseteq U$ of size $n$, if $f$ bijectively maps $S$ into thefirst $n$ natural numbers. These functions are important for many practicalapplications in computing, such as search engines, computer networks, anddatabases. Several algorithms have been proposed to build minimal perfect hashfunctions that: scale well to large sets, retain fast evaluation time, and takevery little space, e.g., 2 - 3 bits/key. PTHash is one such algorithm,achieving very fast evaluation in compressed space, typically several timesfaster than other techniques. In this work, we propose a new constructionalgorithm for PTHash enabling: (1) multi-threading, to either build functionsmore quickly or more space-efficiently, and (2) external-memory processing toscale to inputs much larger than the available internal memory. Only few otheralgorithms in the literature share these features, despite of their bigpractical impact. We conduct an extensive experimental assessment on largereal-world string collections and show that, with respect to other techniques,PTHash is competitive in construction time and space consumption, but retains 2- 6$\times$ better lookup time.

Parallel and External-Memory Construction of Minimal Perfect Hash Functions with PTHash