  In this paper, we consider the generalized min-sum set cover problem,
introduced by Azar, Gamzu, and Yin. Bansal, Gupta, and Krishnaswamy give a
485-approximation algorithm for the problem. We are able to alter their
algorithm and analysis to obtain a 28-approximation algorithm, improving the
performance guarantee by an order of magnitude. We use concepts from
$\alpha$-point scheduling to obtain our improvements.
