Engineering Algorithms for Dynamic Greedy Set Cover

TL;DR

This paper implements and evaluates greedy-based dynamic algorithms for the set cover problem on real-world data, bridging the gap between theoretical results and practical performance.

Contribution

It provides the first comprehensive experimental comparison of dynamic set cover algorithms derived from state-of-the-art frameworks, focusing on practical efficiency and solution quality.

Findings

Algorithms differ significantly in update time and solution quality.

The tradeoff parameter $eta$ influences the balance between efficiency and solution size.

Practical insights identify the most effective strategies for real-world scenarios.

Abstract

In the dynamic set cover problem, the input is a dynamic universe of elements and a fixed collection of sets. As elements are inserted or deleted, the goal is to efficiently maintain an approximate minimum set cover. While the past decade has seen significant theoretical breakthroughs for this problem, a notable gap remains between theoretical design and practical performance, as no comprehensive experimental study currently exists to validate these results. In this paper, we bridge this gap by implementing and evaluating four greedy-based dynamic algorithms across a diverse range of real-world instances. We derive our implementations from state-of-the-art frameworks (such as GKKP, STOC 2017; SU, STOC 2023; SUZ, FOCS 2024), which we simplify by identifying and modifying intricate subroutines that optimize asymptotic bounds but hinder practical performance. We evaluate these algorithms based on solution quality (set cover size) and efficiency, which comprises update time (the time required to update the solution following each insertion or deletion) and recourse (the number of changes made to the solution per update). Each algorithm uses a parameter $\beta$ to balance quality against efficiency; we investigate the influence of this tradeoff parameter on each algorithm and then perform a comparative analysis to evaluate the algorithms against each other. Our results provide the first practical insights into which algorithmic strategies provide the most value in realistic scenarios.