  We study the problem of efficiently and fairly allocating a set of
indivisible goods among agents with identical and additive valuations for the
goods. The objective is to maximize the Nash social welfare, which is the
geometric mean of the agents' valuations. While maximizing the Nash social
welfare is NP-hard, a PTAS for this problem is presented by Nguyen and Rothe.
The main contribution of this paper is to design a first additive PTAS for this
problem, that is, we give a polynomial-time algorithm that maximizes the Nash
social welfare within an additive error $\varepsilon v_{\rm max}$, where
$\varepsilon$ is an arbitrary positive number and $v_{\rm max}$ is the maximum
utility of a good. The approximation performance of our algorithm is better
than that of a PTAS. The idea of our algorithm is simple; we apply a
preprocessing and then utilize an additive PTAS for the target load balancing
problem given recently by Buchem et al. However, a nontrivial amount of work is
required to evaluate the additive error of the output.
