Fair Task Allocation When Cost of Task Is Multidimensional

We consider the problem of fairly allocating indivisible tasks, focusing on a recently introduced notion of fairness called Minmax share guarantee. Minmax share (MMS) is a term of fairness guarantees that is defined to be the minimum cost that an agent can ensure for herself, if she were to partition the tasks into n bundles, and then receive the maximum cost bundle of tasks. However, the cost of tasks considered in previous work is single dimensional, and multidimensional situations have not been researched. In this work, we proposed an allocation algorithm that allocates tasks with multidimensional cost to agents under ordinal model. We prove the approximation ratio of MMS of the algorithm proposed can be guaranteed under 2+m alpha i(1+n)-nn2, in addition the time complexity of the algorithm is O(mlogm). This proposed method is implemented and tested on datasets generated based on a real environment, and the experimental result shows that our algorithm has better performance than existing task allocation algorithms when cost of tasks is multidimensional.