An Algorithmic Framework for Approximating Maximin Share Allocation of Chores

In this paper, we consider the problem of how to fairly dividing m indivisible chores among n agents. The fairness measure we considered here is the maximin share. The previous best known result is that there always exists a frac43 approximation maximin share allocation. With a novel algorithm, we can always find a frac119 approximation maximin share allocation for any instances. We also discuss how to improve the efficiency of the algorithm and its connection to the job scheduling problem.