  An algorithm of the tensor renormalization group is proposed based on a
randomized algorithm for singular value decomposition. Our algorithm is
applicable to a broad range of two-dimensional classical models. In the case of
a square lattice, its computational complexity and memory usage are
proportional to the fifth and the third power of the bond dimension,
respectively, whereas those of the conventional implementation are of the sixth
and the fourth power. The oversampling parameter larger than the bond dimension
is sufficient to reproduce the same result as full singular value decomposition
even at the critical point of the two-dimensional Ising model.
