An improved approximation algorithm for maximin shares

Fair division is a fundamental problem in various multi-agent settings, where the goal to divide set of resources among agents fair manner. We study case m indivisible items need be divided n with additive valuations using popular fairness notion maximin share (MMS). An MMS allocation provides each agent bundle worth at least her share. While it known that such an not exist [1], [2], series remarkable work [3], [4], [5], [6] provided approximation algorithms for 23-MMS which receives 23 times More recently, Ghodsi et al. [7] showed existence 34-MMS and PTAS find (34??)-MMS ?>0. Most previous works utilize intricate require agents' approximate values, are computationally expensive obtain. In this paper, we develop new approach gives simple algorithm showing allocation. Furthermore, our powerful enough easily extended two directions: First, get strongly polynomial time allocation, do values all. Second, show there always exists (34+112n)-MMS improving best factor. This improves guarantee, most notably small n. note 34 was factor n>4.