  Recently Cole and Gkatzelis gave the first constant factor approximation
algorithm for the problem of allocating indivisible items to agents, under
additive valuations, so as to maximize the Nash Social Welfare. We give
constant factor algorithms for a substantial generalization of their problem --
to the case of separable, piecewise-linear concave utility functions. We give
two such algorithms, the first using market equilibria and the second using the
theory of stable polynomials.
  In AGT, there is a paucity of methods for the design of mechanisms for the
allocation of indivisible goods and the result of Cole and Gkatzelis seemed to
be taking a major step towards filling this gap. Our result can be seen as
another step in this direction.
