  We propose very efficient algorithms for the bootstrap percolation and the
diffusion percolation models by extending the Newman-Ziff algorithm of the
classical percolation [M. E. J. Newman and R. M. Ziff, Phys. Rev. Lett. 85
(2000) 4104]. Using these algorithms and the finite-size-scaling, we calculated
with high precision the percolation threshold and critical exponents in the
eleven two-dimensional Archimedean lattices. We present the condition for the
continuous percolation transition in the bootstrap percolation and the
diffusion percolation, and show that they have the same critical exponents as
the classical percolation within error bars in two dimensions. We conclude that
the bootstrap percolation and the diffusion percolation almost certainly belong
to the same universality class as the classical percolation.
