Geometric rounding: a dependent randomized rounding scheme

We develop a new dependent randomized rounding method for approximation of a number of optimization problems with integral assignment constraints. The core of the method is a simple, intuitive, and computationally efficient geometric rounding that simultaneously rounds multiple points in a multi-dimensional simplex to its vertices. Using this method we obtain in a systematic way known as well as new results for the hub location, metric labeling, winner determination and consistent labeling problems. A comprehensive comparison to the dependent randomized rounding method developed by Kleinberg and Tardos [19] and its variants is also conducted, both theoretically and numerically. Overall, our geometric rounding provides a simple and effective alternative for rounding various integer optimization problems.