  Uniform sampling of binary matrix with fixed margins is an important and
difficult problem in statistics, computer science, ecology and so on. The
well-known swap algorithm would be inefficient when the size of the matrix
becomes large or when the matrix is too sparse/dense.
  Here we propose the Rectangle Loop algorithm, a Markov chain Monte Carlo
algorithm to sample binary matrices with fixed margins uniformly. Theoretically
the Rectangle Loop algorithm is better than the swap algorithm in Peskun's
order. Empirically studies also demonstrates the Rectangle Loop algorithm is
remarkablely more efficient than the swap algorithm.
