Smallest suffixient set maintenance in near-real-time

TL;DR

This paper introduces methods for maintaining the smallest suffixient set of a string in near-real-time, using suffix tree algorithms, to measure string repetitiveness efficiently in dynamic settings.

Contribution

It presents algorithms for online maintenance of the smallest suffixient set with polyloglog worst-case time per character, applicable in both left-to-right and right-to-left text processing.

Findings

Achieves near-real-time update times for suffixient set maintenance.

Utilizes Weiner's suffix tree algorithm as a core tool.

Provides frameworks for both left-to-right and right-to-left text streams.

Abstract

The size of the \textit{smallest suffixient set} of positions of a string recently emerged as a new measure of string \textit{repetitiveness} -- a measure reflecting how much of repetitive content the string contains. We study how to maintain the smallest suffixient set online in near-real-time, that is with small (in our case, polyloglog) worst-case time on processing each letter. Two frameworks are considered: when the text is given letter-by-letter in either a right-to-left or left-to-right direction. Our central algorithmic tool is Weiner's suffix tree algorithm and associated algorithmic primitives for its efficient implementation.