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In this note, we propose a m log m algorithm to find the k most probable configurations of a system of n multi-mode independent components, with at most d modes each. m denotes the size of the problem, i.e. max (nd, k). This problem originates in network performance analyzes, in which focusing on the most probable configurations is a means to reduce computational costs. Up to this note, the best known algorithm to extract the most probable configurations was in O(n2d2 + k log k). Our algorithm achieves thus a substantial improvement.