An Asymptotically Optimal Approximation Algorithm for Multiobjective Submodular Maximization at Scale

TL;DR

This paper introduces a scalable, practical approximation algorithm for multiobjective submodular maximization that achieves the best-known guarantees and outperforms existing methods in efficiency and effectiveness.

Contribution

The authors develop the first scalable, practical algorithm for multiobjective submodular maximization with optimal approximation guarantees, addressing computational challenges of previous methods.

Findings

Algorithm outperforms existing methods in objective value.

Algorithm is more scalable and faster.

Introduces a novel application in fair centrality maximization.

Abstract

Maximizing a single submodular set function subject to a cardinality constraint is a well-studied and central topic in combinatorial optimization. However, finding a set that maximizes multiple functions at the same time is much less understood, even though it is a formulation which naturally occurs in robust maximization or problems with fairness considerations such as fair influence maximization or fair allocation. In this work, we consider the problem of maximizing the minimum over many submodular functions, which is known as multiobjective submodular maximization. All known polynomial-time approximation algorithms either obtain a weak approximation guarantee or rely on the evaluation of the multilinear extension. The latter is expensive to evaluate and renders such algorithms impractical. We bridge this gap and introduce the first scalable and practical algorithm that obtains the best-known approximation guarantee. We furthermore introduce a novel application fair centrality maximization and show how it can be addressed via multiobjective submodular maximization. In our experimental evaluation, we show that our algorithm outperforms known algorithms in terms of objective value and running time.