Smallest suffixient set maintenance in near-real-time

2026-04-30

AI Summary

This work addresses the problem of dynamically maintaining a minimal suffix-rich set for a string under near-real-time constraints to efficiently quantify its repetitiveness. Focusing on online scenarios where characters arrive one by one—either left-to-right or right-to-left—it presents the first algorithm achieving polyloglog worst-case time per character update. The approach leverages Weiner’s suffix tree and its fundamental algorithmic primitives to establish a core maintenance mechanism, thereby enabling, for the first time, efficient dynamic maintenance of minimal suffix-rich sets under bidirectional streaming input. This breakthrough substantially extends the applicability of string repetitiveness measures to dynamic environments.

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.

Problem

• smallest suffixient set
• string repetitiveness
• near-real-time
• online maintenance
• suffix tree

Innovation

• smallest sufficient set
• near-real-time
• online maintenance
• Weiner's suffix tree
• string repetitiveness