Abstract
Submodular function maximization, a crucial aspect of combinatorial optimization, is extensively applied in various fields like economics and computing. Recently, the focus has shifted towards the generalizations of submodular maximization problems, such as k-submodular function maximization. This approach not only considers the selection of elements from the ground set but also the specific k-set they belong to. It has been proved useful in modeling several machine learning problems, including influence maximization with k topics and sensor placement with k types of sensors. In real-world applications, elements possess certain attributes like gender, age, race, etc., which are used to group elements in the ground set. To maintain fairness, it is desirable to have a balanced number of elements in each group, introducing the concept of group fairness. We divide the ground set V into m groups \(\left( V_{1},V_{2},...,V_{m} \right) \), each representing items with the same attribute. If the difference in the number of elements between any two groups is less than or equal to \(\alpha \), we say the group fairness constraints are satisfied. Existing k-submodular algorithms do not account for the group fairness constraints, leading to imbalances in group sizes. This paper addresses this gap by studying k-submodular maximization under the fairness constraints. We explore the k-submodular maximization problem under the intersection of the fairness constraints and total size constraint, achieving an approximate ratio of 1/2 for monotone cases and 1/24 for non-monotone cases.
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Hu, W., Liu, B. (2024). Approximation Algorithms for k-Submodular Maximization Under the Fair Constraints and Size Constraints. In: Ghosh, S., Zhang, Z. (eds) Algorithmic Aspects in Information and Management. AAIM 2024. Lecture Notes in Computer Science, vol 15179. Springer, Singapore. https://doi.org/10.1007/978-981-97-7798-3_20
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