Re-identification is usually defined as the problem of deciding whether a person currently in the field of view of a camera has been seen earlier either by that camera or another. However, a different version of the problem arises even when people are seen by multiple cameras with overlapping fields of view. Current tracking algorithms can easily get confused when people come close to each other and merge trajectory fragments into trajectories that include erroneous identity switches. Preventing this means re-identifying people across trajectory fragments. In this chapter, we show that this can be done very effectively by formulating the problem as a minimum-cost maximum-flow linear program. This version of the re-identification problem can be solved in real-time and produces trajectories without identity switches. We demonstrate the power of our approach both in single- and multi-camera setups to track pedestrians, soccer players, and basketball players.