Smallest Suffixient Sets as a Repetitiveness Measure

2025-06-05

AI Summary

Existing string repetitiveness measures lack metrics that simultaneously capture structural regularity and computational tractability. Method: We introduce the *suffixient set*—a novel structural representation of repetitiveness—and define its minimum cardinality χ as a new repetitiveness measure. Leveraging combinatorial string analysis and compressed data structure theory, we rigorously establish that χ lies between the LZ77 parsing size and the smallest grammar size. Contribution/Results: χ bridges a theoretical gap by providing the first structured repetitiveness measure grounded in random-access capability. It is computable in polynomial time, admits precise theoretical placement within the hierarchy of compression-based measures, and exhibits fine-grained sensitivity to edit operations (e.g., insertions and deletions). This work establishes a new theoretical foundation and practical metric for indexing repetitive texts, pattern matching, and compression-aware algorithm design.

Technology Category

• Data Mining & Knowledge Management: Data Compression
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Evaluation and Analysis

Application Category

• Web Mining and Content Analysis: Web measurements
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Suffixient sets are a novel combinatorial object that capture the essential information of repetitive strings in a way that, provided with a random-access mechanism, supports various forms of pattern matching. In this paper we study the size $chi$ of the smallest suffixient set as a repetitiveness measure: we place it between known measures and study its sensitivity to various string operations.

Problem

• Study smallest suffixient sets as repetitiveness measure
• Compare suffixient sets with known repetitiveness measures
• Analyze sensitivity of suffixient sets to string operations

Innovation

• Novel suffixient sets for repetitive strings
• Smallest suffixient set as repetitiveness measure
• Supports pattern matching with random-access