  The max-min fair allocation problem seeks an allocation of resources to
players that maximizes the minimum total value obtained by any player. Each
player $p$ has a non-negative value $v_{pr}$ on resource $r$. In the restricted
case, we have $v_{pr}\in \{v_r, 0\}$. That is, a resource $r$ is worth value
$v_r$ for the players who desire it and value 0 for the other players. In this
paper, we consider the configuration LP, a linear programming relaxation for
the restricted problem. The integrality gap of the configuration LP is at least
$2$. Asadpour, Feige, and Saberi proved an upper bound of $4$. We improve the
upper bound to $23/6$ using the dual of the configuration LP. Since the
configuration LP can be solved to any desired accuracy $\delta$ in polynomial
time, our result leads to a polynomial-time algorithm which estimates the
optimal value within a factor of $23/6+\delta$.
