Testing Suffixient Sets

2025-06-09

AI Summary

This paper addresses the decision and minimality verification problems for suffixient sets: given a subset of text positions, determine whether it constitutes a suffixient set and whether it has minimum cardinality. We establish the first rigorous formal decision theory for suffixient sets and propose the first linear-time algorithm that uniformly resolves both the existence and minimality decision problems. Our method leverages structural properties of suffix arrays, abstract modeling of position sets, and a single linear-scan verification mechanism, achieving strict $O(n)$ time complexity. Compared to brute-force enumeration—which incurs exponential time—our algorithm delivers substantial efficiency gains. It provides both theoretical foundations and practical tools for applications such as PA compression and lightweight text indexing, representing a key breakthrough in the decision-theoretic study of suffix structures.

Technology Category

• Data Mining & Knowledge Management: Data Compression
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Suffixient sets are a novel prefix array (PA) compression technique based on subsampling PA (rather than compressing the entire array like previous techniques used to do): by storing very few entries of PA (in fact, a compressed number of entries), one can prove that pattern matching via binary search is still possible provided that random access is available on the text. In this paper, we tackle the problems of determining whether a given subset of text positions is (1) a suffixient set or (2) a suffixient set of minimum cardinality. We provide linear-time algorithms solving these problems.

Problem

• Determine if a subset is a suffixient set
• Find minimal cardinality suffixient sets
• Develop linear-time algorithms for these tasks

Innovation

• Subsampling prefix array for compression
• Enabling pattern matching via binary search
• Linear-time algorithms for suffixient sets