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On the binary erasure channel, the performance of LDPC codes decoded by iterative algorithms is estimated by small-size stopping sets. We have proposed a probabilistic algorithm for computing the minimum size of stopping sets of LDPC codes. In this paper, we analyze the probability and the complexity of finding the minimum-size stopping sets, and give an error probability of determining the minimum size of stopping sets after processing our algorithm. Additionally, we show the numerical results of computing the minimum size of stopping sets of several LDPC codes. In these result, we could compute the minimum size of stopping sets with high reliability.