@article{Bredereck_Faliszewski_Kaczmarczyk_Knop_Niedermeier_2020, title={Parameterized Algorithms for Finding a Collective Set of Items}, volume={34}, url={https://ojs.aaai.org/index.php/AAAI/article/view/5551}, DOI={10.1609/aaai.v34i02.5551}, abstractNote={<p> We extend the work of Skowron et al. (AIJ, 2016) by considering the parameterized complexity of the following problem. We are given a set of items and a set of agents, where each agent assigns an integer utility value to each item. The goal is to find a set of <em>k</em> items that these agents would collectively use. For each such collective set of items, each agent provides a score that can be described using an OWA (ordered weighted average) operator and we seek a set with the highest total score. We focus on the parameterization by the number of agents and we find numerous fixed-parameter tractability results (however, we also find some W[1]-hardness results). It turns out that most of our algorithms even apply to the setting where each agent has an integer weight.</p>}, number={02}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Bredereck, Robert and Faliszewski, Piotr and Kaczmarczyk, Andrzej and Knop, DuĊĦan and Niedermeier, Rolf}, year={2020}, month={Apr.}, pages={1838-1845} }