# Group Fairness for Knapsack Problems

arXiv: https://arxiv.org/abs/2006.07832 · HTML: https://mlsanity.com/paper/2006.07832/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2020.

## Built on by (most cited first, 3 of 3)

- [DiRe Committee : Diversity and Representation Constraints in Multiwinner Elections](https://mlsanity.com/paper/2107.07356/) (2021)
- [Time Fairness in Online Knapsack Problems](https://mlsanity.com/paper/2305.13293/) (2023)
- [Multiple Fairness and Cardinality constraints for Students-Topics Grouping Problem](https://mlsanity.com/paper/2206.09895/) (2022)

## Abstract (arXiv)

We study the knapsack problem with group fairness constraints. The input of the problem consists of a knapsack of bounded capacity and a set of items, each item belongs to a particular category and has and associated weight and value. The goal of this problem is to select a subset of items such that all categories are fairly represented, the total weight of the selected items does not exceed the capacity of the knapsack,and the total value is maximized. We study the fairness parameters such as the bounds on the total value of items from each category, the total weight of items from each category, and the total number of items from each category. We give approximation algorithms for these problems. These fairness notions could also be extended to the min-knapsack problem. The fair knapsack problems encompass various important problems, such as participatory budgeting, fair budget allocation, advertising.