On complexity of Shmoys - Swamy class of two-stage linear stochastic programming problems

We consider a class of two-stage linear stochastic programming problems, introduced by Shmoys and Swamy [4], motivated by a relaxation of a stochastic set cover problem. We show that the sample size required to solve this problem by the sample average approximation (SAA) method with a relative accuracy κ > 0 and confidence 1 − α is polynomial in κ, log(α−1), dimensions of the problem and a certain parameter λ. This implies that such problems can be solved in time polynomial in these parameters, the result obtained in [4] by a different method. ∗Georgia Institute of Technology, Atlanta, Georgia 30332, USA, [email protected] †Georgia Institute of Technology, Atlanta, Georgia 30332, USA, [email protected]. Research of this author was partly supported by the NSF grant DMS-0510324.