{"type":"ScholarlyArticle","title":"Complexity of Efficient and Envy-Free Resource Allocation: Few Agents, Resources, or Utility Levels","authors":[{"name":"Bernhard Bliem","slug":"bernhard-bliem","given":"Bernhard","family":"Bliem","affiliation":""},{"name":"Robert Bredereck","slug":"robert-bredereck","given":"Robert","family":"Bredereck","affiliation":""},{"name":"Rolf Niedermeier","slug":"rolf-niedermeier","given":"Rolf","family":"Niedermeier","affiliation":""}],"abstract":"We study the problem of finding a Pareto-efficient and envy-free allocation of a set of indivisible resources to a set of agents with monotonic preferences, either dichotomous or additive. Motivated by results of Bouveret and Lang [JAIR 2008], we provide a refined computational complexity analysis by studying the influence of three natural parameters: the number n of agents, the number m of resources, and the number z of different numbers occurring in utility-based preferences of the agents. On the negative side, we show that small values for n and z alone do not significantly lower the computational complexity in most cases. On the positive side, devising fixed-parameter algorithms we show that all considered problems are tractable in case of small m. Furthermore, we develop a fixed-parameter algorithm indicating that the problem with additive preferences becomes computationally tractable in case of small n and small z.","doi":null,"url":"https://ijcai.org/proceedings/2016/22","pdf":"https://ijcai.org/proceedings/2016/0022.pdf","markdown":"https://ijcai.org/proceedings/2016/22.md","bibtex":"https://ijcai.org/proceedings/2016/bibtex/22","volume":{"slug":"2016","title":"Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2016","url":"https://ijcai.org/proceedings/2016/","year":2016,"location":"New York, NY, USA","dates":"9–15 July 2016","editors":"Subbarao Kambhampati","isbn":"978-1-57735-770-4; 978-1-57735-771-1","publisher":"AAAI Press / International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":22,"pages":{"first":102,"last":107},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}