About: Efficient approximately-fair item allocation

When allocating objects among people with different preferences, two major goals are Pareto efficiency and fairness. Since the objects are indivisible, there may not exist any fair allocation. For example, when there is a single house and two people, every allocation of the house will be unfair to one person. Therefore, several common approximations have been studied, such as maximin-share fairness (MMS), envy-freeness up to one item (EF1), proportionality up to one item (PROP1), and equitability up to one item (EQ1). The problem of efficient approximately-fair item allocation is to find an allocation that is both Pareto-efficient (PE) and satisfies one of these fairness notions. The problem was first presented at 2016 and has attracted considerable attention since then.