FO-Query Enumeration over SLP-Compressed Structures of Bounded Degree

TL;DR

This paper presents an efficient enumeration algorithm for first-order query results over bounded degree structures represented in highly compressed form by straight-line programs, achieving linear preprocessing and constant delay.

Contribution

It extends enumeration results to structures compressed by SLPs under the apex condition, with linear preprocessing and constant delay for fixed formulas.

Findings

Enumeration with linear preprocessing and constant delay over SLP-compressed structures.

Algorithm works for structures satisfying the apex condition.

Applicable to highly compressed relational data representations.

Abstract

Enumerating the result set of a first-order query over a relational structure of bounded degree can be done with linear preprocessing and constant delay. In this work, we extend this result towards the compressed perspective where the structure is given in a potentially highly compressed form by a straight-line program (SLP). Our main result is an algorithm that enumerates the result set of a first-order query over a structure of bounded degree that is represented by an SLP satisfying the so-called apex condition. For a fixed formula, the enumeration algorithm has constant delay and needs a preprocessing time that is linear in the size of the SLP.