Multiple target tracking (MTT) is a well-studied technique in the field of radar technology, which associates anonymized measurements with the appropriate object trajectories. This technique, however, suffers from combinatorial explosion, since each new measurement may potentially be associated with any of the existing tracks. Consequently, the complexity of existing MTT algorithms grows exponentially with the number of objects, rendering them inapplicable to large databases. In this paper, we investigate the feasibility of applying the MTT framework in the context of large trajectory databases. Given a history of object movements, where the corresponding object ids have been removed, our goal is to track the trajectory of every object in the database in successive timestamps. Our main contribution lies in the transition from an exponential solution to a polynomial one. We introduce a novel method that transforms the tracking problem into a min-cost max-flow problem. We then utilize well-known graph algorithms that work in polynomial time with respect to the number of objects. The experimental results indicate that the proposed methods produce high quality results that are comparable with the state-of-the-art MTT algorithms. In addition, our methods reduce significantly the computational cost and scale to a large number of objects.