The trade algorithm, which includes the curveball and fastball implementations, is the state-of-the-art for uniformly sampling r x c binary matrices with fixed row and column sums. The mixing time of the trade algorithm is currently unknown, although 5r is currently used as a heuristic. We propose a distribution-based approach to estimating the mixing time, but which also can return a sample of matrices that are nearly guaranteed to be uniformly randomly sampled. In numerical experiments on matrices that vary by size, fill, and row and column sum distributions, we find that the upper bound on mixing time is at least 10r, and that it increases as a function of both c and the fraction of cells containing a 1.

翻译：trade算法（包括curveball和fastball实现）是当前对具有固定行和列和的r×c二进制矩阵进行均匀抽样的最先进方法。目前该算法的混合时间尚属未知，尽管实际中常使用5r作为启发式估计。我们提出一种基于分布的混合时间估算方法，该方法同时能够返回一个几乎保证均匀随机抽样的矩阵样本。在对不同规模、填充度以及行列和分布的矩阵进行的数值实验中，我们发现混合时间上界至少为10r，并且该上界随着矩阵列数c和单元格中1的占比增加而增大。