Fast Compressed Tries through Path Decompositions

TL;DR

This paper introduces new succinct, path-decomposed trie representations that significantly reduce space and improve speed in string dictionaries and monotone minimal perfect hash functions, outperforming existing methods.

Contribution

It presents novel compressed trie structures using path decompositions, achieving better space efficiency and faster query times for specific string applications.

Findings

Outperforms state-of-the-art compressed dictionaries in space efficiency.

Achieves competitive query times with practical data structures.

Runs several times faster than existing trie-based monotone perfect hash functions.

Abstract

Tries are popular data structures for storing a set of strings, where common prefixes are represented by common root-to-node paths. Over fifty years of usage have produced many variants and implementations to overcome some of their limitations. We explore new succinct representations of path-decomposed tries and experimentally evaluate the corresponding reduction in space usage and memory latency, comparing with the state of the art. We study two cases of applications: (1) a compressed dictionary for (compressed) strings, and (2) a monotone minimal perfect hash for strings that preserves their lexicographic order. For (1), we obtain data structures that outperform other state-of-the-art compressed dictionaries in space efficiency, while obtaining predictable query times that are competitive with data structures preferred by the practitioners. In (2), our tries perform several times faster than other trie-based monotone perfect hash functions, while occupying nearly the same space.