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

Abstract

Given a dynamic set $\mathcal{K}$ 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 $\mathcal{K}$ that provides lookup, prefix search, and update operations on $\mathcal{K}$. Under the assumption that $\alpha =w/\lg \sigma$ characters fit into a single machine word of w bits, we propose a keyword dictionary that represents $\mathcal{K}$ in either $n\lg \sigma +\mathrm{\Theta }(k\lg n)$ or $|T|\lg \sigma +\mathrm{\Theta }(kw)$ bits of space, where $|T|$ is the number of nodes of a trie representing $\mathcal{K}$. It supports all operations in $\mathcal{O}(m/\alpha +\lg \alpha )$ 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.