Solutions for object tracking problems are presented by gathering images using one or more cameras, processing the gathered images to generate a directed acyclic graph, using the directed acyclic graph to determine a path cover that achieves maximum weight and satisfies one or more positive or negative constraints, and using the path cover to solve the object tracking problem. A first set of solutions utilizes trellis graphs, a second set of solutions employs a greedy approach, and a third set of solutions uses search algorithms.