An $O(k \log{n})$ algorithm for prefix based ranked autocomplete

TL;DR

This paper introduces an efficient algorithm with $O(k \u2217 \u2217log n)$ complexity for providing top-ranked autocomplete suggestions based on user-typed prefixes, optimizing search suggestion retrieval.

Contribution

It presents a novel algorithm that significantly improves the efficiency of prefix-based ranked autocomplete suggestions with optimal time and space complexity.

Findings

Achieves $O(k  log n)$ runtime for top-k suggestions

Uses $O(n)$ space for storing suggestions

Enhances search suggestion responsiveness

Abstract

Many search engines such as Google, Bing & Yahoo! show search suggestions when users enter search phrases on their interfaces. These suggestions are meant to assist the user in finding what she wants quickly and also suggesting common searches that may result in finding information that is more relevant. It also serves the purpose of helping the user if she is not sure of what to search for, but has a vague idea of what it is that she wants. We present an algorithm that takes time proportional to $O(k \log{n})$, and $O(n)$ extra space for providing the user with the top $k$ ranked suggestions out of a corpus of $n$ possible suggestions based on the prefix of the query that she has entered so far.