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An optimal causal message ordering algorithm for asynchronous distributed systems was proposed by Kshemkalyani and Singhal and its optimality was proven theoretically. For a system of n processes, although the space complexity of this algorithm was shown to be O(n2) integers, it was expected that the actual space overhead would be much less than n2. It is difficult to determine the behavior of this algorithm by a theoretical analysis. We measure the overheads of two different implementations of the optimal causal message ordering algorithm via simulation under a wide range of system conditions. The optimal algorithm is seen to display significantly less message space overhead and log space overhead than the canonical Raynal-Schiper-Toueg algorithm.