{"type":"ScholarlyArticle","title":"Fair Submodular Maximization over a Knapsack Constraint","authors":[{"name":"Lijun Li","slug":"lijun-li","given":"Lijun","family":"Li","affiliation":""},{"name":"Chenyang Xu","slug":"chenyang-xu","given":"Chenyang","family":"Xu","affiliation":""},{"name":"Liuyi Yang","slug":"liuyi-yang","given":"Liuyi","family":"Yang","affiliation":""},{"name":"Ruilong Zhang","slug":"ruilong-zhang","given":"Ruilong","family":"Zhang","affiliation":""}],"abstract":"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).\r\n\r\nWhile 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.","doi":"10.24963/ijcai.2025/438","url":"https://ijcai.org/proceedings/2025/438","pdf":"https://ijcai.org/proceedings/2025/0438.pdf","markdown":"https://ijcai.org/proceedings/2025/438.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/438","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":438,"pages":{"first":3934,"last":3942},"keywords":["Game Theory and Economic Paradigms: GTEP: Computational social choice","Agent-based and Multi-agent Systems: MAS: Resource allocation"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}