Compressed Set Representations based on Set Difference

2026-01-30

AI Summary

This work addresses the challenge of efficiently compressing multiple sets while supporting fast queries. The authors propose a compression scheme based on inter-set differences, leveraging a minimum spanning tree (MST) to optimize differential encoding across sets, thereby significantly improving compression efficiency. They further design a data structure that supports fundamental operations—including membership testing, predecessor/successor queries, and random access—all executed in logarithmic time. Experimental results demonstrate that the proposed method outperforms existing standard approaches in both construction speed and query performance, achieving an effective balance between space efficiency and time efficiency.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

We introduce a compressed representation of sets of sets that exploits how much they differ from each other. Our representation supports access, membership, predecessor and successor queries on the sets within logarithmic time. In addition, we give a new MST-based construction algorithm for the representation that outperforms standard ones.

Problem

• compressed set representations
• set difference
• set of sets
• efficient queries

Innovation

• compressed set representation
• set difference
• MST-based construction
• logarithmic-time queries
• succinct data structures