Engineering Algorithms for Dynamic Greedy Set Cover

2026-04-03

AI Summary

This work addresses the dynamic set cover problem, which requires efficiently maintaining an approximately optimal solution under frequent insertions and deletions of elements—a setting where existing theoretical algorithms lack empirical validation. For the first time, we present a systematic experimental evaluation of state-of-the-art dynamic algorithms based on greedy strategies, originating from GKKP (2017), SU (2023), and SUZ (2024). By simplifying complex subroutines and introducing a tunable parameter β to balance solution quality against computational efficiency, we enable practical deployment of these methods. Extensive experiments on real-world datasets reveal significant differences among the algorithms in terms of cover size, update time, and amortized overhead, offering the first empirical guidance for selecting and configuring dynamic set cover algorithms in practical applications.

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 $β$ 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.

Problem

• dynamic set cover
• greedy algorithms
• approximation algorithms
• experimental evaluation
• update time

Innovation

• dynamic set cover
• greedy algorithms
• practical evaluation
• update time
• recourse