Compressed Set Representations based on Set Difference

TL;DR

This paper presents a novel compressed data structure for representing collections of sets that efficiently exploits their differences, enabling fast queries and improved construction algorithms.

Contribution

Introduces a new compressed set-of-sets representation based on set differences, with logarithmic query support and an MST-based construction method.

Findings

Supports access, membership, predecessor, and successor queries in logarithmic time.

Outperforms standard set representation methods in construction efficiency.

Provides a new MST-based algorithm for building the data structure.

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.