The Fair OWA One-to-One Assignment Problem: NP-Hardness and Polynomial Time Special Cases
- 46 Downloads
We consider a one-to-one assignment problem consisting of matching n objects with n agents. Any matching leads to a utility vector whose n components measure the satisfaction of the various agents. We want to find an assignment maximizing a global utility defined as an ordered weighted average (OWA) of the n individual utilities. OWA weights are assumed to be non-increasing with ranks of satisfaction so as to include an idea of fairness in the definition of social utility. We first prove that the problem is NP-hard; then we propose a polynomial algorithm under some restrictions on the set of admissible weight vectors, proving that the problem belongs to XP.
KeywordsAssignment problem Fairness Ordered weighted average Complexity
The referees are gratefully acknowledged for their constructive comments and suggestions which resulted in an improved presentation of the paper.
- 1.Aziz, H., Gaspers, S., Mackenzie, S., Walsh, T.: Fair assignment of indivisible objects under ordinal preferences. In: Proceedings of the 13th International Conference on Autonomous Agents and Multiagent Systems, pp. 1305–1312 (2014)Google Scholar
- 4.Bouveret, S., Lemaître, M., Fargier, H., Lang, J.: Allocation of indivisible goods: a general model and some complexity results. In: Proceedings of the 4th International Joint Conference on Autonomous Agents and Multiagent Systems, pp. 1309–1310 (2005)Google Scholar
- 8.Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the 3rd Annual ACM Symposium on Theory of Computing, pp. 151–158. ACM (1971)Google Scholar
- 13.Golden, B., Perny, P.: Infinite order Lorenz dominance for fair multiagent optimization. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, pp. 383–390 (2010)Google Scholar
- 15.Gourvès, L., Monnot, J., Tlilane, L.: A matroid approach to the worst case allocation of indivisible goods. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence, pp. 136–142 (2013)Google Scholar
- 19.Heinen, T., Nguyen, N.T., Rothe, J.: Fairness and rank-weighted utilitarianism in resource allocation. In: Proceedings of the 4th International Conference on Algorithmic Decision Theory, pp. 521–536 (2015)Google Scholar
- 23.Lesca, J., Perny, P.: LP Solvable Models for Multiagent Fair Allocation problems. In: Proceedings of the 19th European Conference on Artificial Intelligence, pp. 387–392 (2010)Google Scholar