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In multiple-object tracking applications, it is essential to address the problem of associating targets and observation data. For visual tracking of multiple targets which involves objects that split and merge, a target may be associated with multiple measurements and many targets may be associated with a single measurement. The space of such data association is exponential in the number of targets and exhaustive enumeration is impractical. We pose the association problem as a bipartite graph edge covering problem given the targets and the object detection information. We propose an efficient method of maintaining multiple association hypotheses with the highest probabilities over all possible histories of associations. Our approach handles objects entering and exiting the field of view, merging and splitting objects, as well as objects that are detected as fragmented parts. Experimental results are given for tracking multiple players in a soccer game and for tracking people with complex interaction in a surveillance setting. It is shown through quantitative evaluation that our method tracks through varying degrees of interactions among the targets with high success rate.