Message passing algorithms for facility location problems

Discrete location analysis is one of the most widely studied branches of operations research, whose applications arise in a wide variety of settings. This thesis describes a powerful new approach to facility location problems - that of message passing inference in probabilistic graphical models. Using this framework, we develop new heuristic algorithms, as well as a new approximation algorithm for a particular problem type. In machine learning applications, facility location can be seen a discrete formulation of clustering and mixture modeling problems. We apply the developed algorithms to such problems in computer vision. We tackle the problem of motion segmentation in video sequences by formulating it as a facility location instance and demonstrate the advantages of message passing algorithms over current segmentation methods.