Fair Submodular Maximization over a Knapsack Constraint
Fair Submodular Maximization over a Knapsack Constraint
Lijun Li, Chenyang Xu, Liuyi Yang, Ruilong Zhang
Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence
Main Track. Pages 3934-3942.
https://doi.org/10.24963/ijcai.2025/438
We consider fairness in submodular maximization subject to a knapsack constraint, a fundamental problem with various applications in economics, machine learning, and data mining. In the model, we are given a set of ground elements, each associated with a cost and a color, and a monotone submodular function defined over them. The goal is to maximize the submodular function while guaranteeing that the total cost does not exceed a specified budget (the knapsack constraint) and that the number of elements selected for each color falls within a designated range (the fairness constraint).
While there exists some recent literature on this topic, the existence of a non-trivial approximation for the problem -- without relaxing either the knapsack or fairness constraints -- remains a challenging open question. This paper makes progress in this direction. We demonstrate that when the number of colors is constant, there exists a polynomial-time algorithm that achieves a constant approximation with high probability. Additionally, we show that if either the knapsack or fairness constraint is relaxed only to require expected satisfaction, a tight approximation ratio of (1-1/e-epsilon) can be obtained in expectation for any epsilon >0.
Keywords:
Game Theory and Economic Paradigms: GTEP: Computational social choice
Agent-based and Multi-agent Systems: MAS: Resource allocation
