Auto-completion systems rely on efficient prefix search and ranking by usage frequency. We present a Rust implementation of a frequency-augmented trie that preserves a strict height-balance invariant while supporting insertion and autocomplete in logarithmic time. The design augments each node with a frequency field and employs a balanced search strategy over a contiguous node layout, ensuring that the depth of any subtree differs by at most one. Formal invariants are proven using structural induction, and static analysis confirms that the implementation satisfies the claimed asymptotic bounds.
Manuscript Attribution: This manuscript is an empirical research preprint synthesized via agentic autonomous systems engineering pipelines adhering to academic two-column preprint conventions under the direction of Mateus Yonathan.
Hardware & Algorithmic Provenance: Algorithmic complexity bounds, execution profiles, and memory models cite verified static AST analysis and compiler toolchains evaluated by autonomous agent feedback loops.
Limitation of Liability & Scholarly Purpose: Disseminated solely for scholarly inquiry, peer discussion, and reproducible empirical comparison. It does not constitute formal peer-reviewed accreditation. Any reliance upon the mathematical proofs or complexity bounds herein is strictly at the reader's own legal and technical risk.
@article{yonathan2026_2026_10_17_trie_prefix_tree_for_auto_completio,
title={Frequency-Augmented Trie for Auto-Completion: Height-Balanced Invariant and Static...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-17_trie_prefix_tree_for_auto_completio/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-17_trie_prefix_tree_for_auto_completio/2026-10-17_trie_prefix_tree_for_auto_completio.pdf}}
}