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In this paper we are investigating the capacity of Mobile Ad Hoc Networks under a concurrent transmission constraint imposed by common MAC layer protocols (such as 802.11). This problem is known to be an NP-hard combinatorial problem and a greedy algorithm has been proposed for solving it in polynomial time. We propose an efficient algorithm for solving the exact problem and compare the exact and approximate solutions for a variety of network sizes and node distributions (resulting from commonly used mobility models). Our findings confirm that the greedy solution provides a good approximation of the exact solution even for small network sizes. Based on the exact solution, we also derive an empirical formula that relates the capacity optimizing transmission range to the number of wireless nodes uniformly distributed in a square unit area.