Title: MIP Formulations for the Steiner Forest Problem,
Abstract: The Steiner Forest problem is among the fundamental network design problems.
Finding tight linear programming bounds for the problem is the key for both
fast Branch-and-Bound algorithms and good primal-dual approximations. On the
theoretical side, the best known bound can be obtained from an integer program
[KLSv08]. It guarantees a value that is a (2-eps)-approximation of the integer
optimum. On the practical side, bounds from a mixed integer program by Magnanti
and Raghavan [MR05] are very close to the integer optimum in computational
experiments, but the size of the model limits its practical usefulness. We
compare a number of known integer programming formulations for the problem and
propose three new formulations. We can show that the bounds from our two new
cut-based formulations for the problem are within a factor of 2 of the integer
optimum. In our experiments, the formulations prove to be both tractable and
provide better bounds than all other tractable formulations. In particular, the
factor to the integer optimum is much better than 2 in the experiments.