Consistent Submodular Maximization

TL;DR

This paper addresses the challenge of maintaining high-quality, stable solutions for monotone submodular maximization in streaming environments with consistency constraints, balancing approximation accuracy and solution stability.

Contribution

It introduces algorithms that achieve different trade-offs between solution consistency and approximation quality in dynamic streaming settings.

Findings

Algorithms effectively balance stability and approximation in practice.

Theoretical guarantees are supported by experimental results.

Algorithms outperform baseline methods in real-world data.

Abstract

Maximizing monotone submodular functions under cardinality constraints is a classic optimization task with several applications in data mining and machine learning. In this paper we study this problem in a dynamic environment with consistency constraints: elements arrive in a streaming fashion and the goal is maintaining a constant approximation to the optimal solution while having a stable solution (i.e., the number of changes between two consecutive solutions is bounded). We provide algorithms in this setting with different trade-offs between consistency and approximation quality. We also complement our theoretical results with an experimental analysis showing the effectiveness of our algorithms in real-world instances.