In computer science and operations research, the envy minimization problem is the problem of allocating discrete items among agents with different valuations over the items, such that the amount of envy is as small as possible.
There are several ways to define the objective function (the amount of envy) for minimization.
Some of them are: With general valuations, any deterministic algorithm that minimizes the maximum envy-ratio requires a number of queries which is exponential in the number of goods in the worst case.
Benade, Kazachkov, Procaccia and Psomas[5] consider the problem of minimizing the maximum envy-difference, where the valuations are normalized such that the value of each item is in [0,1].
Jiang, Kulkarni and Singla[6] improve their envy bound using an algorithm for online two-dimensional discrepancy minimization.