In this paper, we show that tracking multiple people whose paths may intersect can be formulated as a multi-commodity network flow problem. Our proposed framework is designed to exploit image appearance cues to prevent identity switches. Our method is effective even when such cues are only available at distant time intervals. This is unlike many current approaches that depend on appearance being exploitable from frame-to-frame. Furthermore, our algorithm lends itself to a real-time implementation. We validate our approach on three publicly available datasets that contain long and complex sequences, the APIDIS basketball dataset, the ISSIA soccer dataset, and the PETS'09 pedestrian dataset. We also demonstrate its performance on a newer basketball dataset that features complete world championship basketball matches. In all cases, our approach preserves identity better than state-of-the-art tracking algorithms.