Stochastic Probing with Increasing Precision.

We consider a selection problem with stochastic probing. There is a set of items whose values are drawn from independent distributions. The distributions are known in advance. Each item can be \emph{tested} repeatedly. Each test reduces the uncertainty about the realization of its value. We study a testing model, where the first test reveals if the realized value is smaller or larger than the median of the underlying distribution. Subsequent tests allow to further narrow down the interval in which the realization is located. There is a limited number of possible tests, and our goal is to design near-optimal testing strategies that allow to maximize the expected value of the chosen item. We study both identical and non-identical distributions and develop polynomial-time algorithms with constant approximation factors in both scenarios.