Surveillance systems are often required to simultaneously estimate the trajectory parameters of several targets. This problem is complicated significantly in high target density situations since the individual data sequences required by standard estimation algorithms are difficult to form. This paper discusses certain computational aspects of assigning closely spaced sensor returns to individual tracks. We refer to this as a "multiple choice" estimation problem since the real tracks are generally hidden in a large set F of feasible tracks. Forming the feasible track set F on the basis of a priori knowledge of the problem is the first step on the assignment process. A subset of the potential tracks contained in F is then selected on the basis accomplished by 0-1 integer programming, as we now illustrate for a simple discrete linear problem.