C-trie++: A dynamic trie tailored for fast prefix searches

Abstract

Given a dynamic set K of k strings of total length n whose characters are drawn from an alphabet of size σ, a keyword dictionary is a data structure built on K that provides lookup, prefix search, and update operations on K. Under the assumption that α=w/lg⁡σ characters fit into a single machine word of w bits, we propose a keyword dictionary that represents K in either nlg⁡σ+Θ(klg⁡n) or |T|lg⁡σ+Θ(kw) bits of space, where |T| is the number of nodes of a trie representing K. It supports all operations in O(m/α+lg⁡α) expected time on an input string of length m in the word RAM model. An evaluation of our implementation highlights the practical usefulness of the proposed data structure, especially for prefix searches — one of the most essential keyword dictionary operations.