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In this paper we present a linear programming (LP) based approach for solving the data association problem (DAP) in multiple target tracking. It is well-known that the DAP can be formulated as an integer program. We present a compact formulation of the DAP. To solve practical instances of the DAP we propose an algorithm that uses an iterated K-scan sliding window technique. In each iteration we solve the linear programming relaxation of an integer program and next apply a greedy rounding procedure. Computational experiments indicate that the quality of the solutions found is quite satisfactory.