Data Summarization beyond Monotonicity: Non-monotone Two-Stage Submodular Maximization

TL;DR

This paper extends the two-stage submodular maximization framework to non-monotone functions, providing the first constant-factor approximation algorithms for this more general and realistic setting.

Contribution

It introduces the first constant-factor approximation algorithms for non-monotone two-stage submodular maximization, broadening the applicability of the method.

Findings

First algorithms for non-monotone case

Constant-factor approximation guarantees

Applicable to data summarization tasks

Abstract

The objective of a two-stage submodular maximization problem is to reduce the ground set using provided training functions that are submodular, with the aim of ensuring that optimizing new objective functions over the reduced ground set yields results comparable to those obtained over the original ground set. This problem has applications in various domains including data summarization. Existing studies often assume the monotonicity of the objective function, whereas our work pioneers the extension of this research to accommodate non-monotone submodular functions. We have introduced the first constant-factor approximation algorithms for this more general case.