  We construct a rejection-free Monte Carlo method for the hard-disk system.
Rejection-free Monte Carlo methods preserve the time-evolution behavior of the
standard Monte Carlo method, and this relationship is confirmed for our method
by observing nonequilibrium relaxation of a bond-orientational order parameter.
The rejection-free method gives a greater computational efficiency than the
standard method at high densities. The rejection free method is implemented in
a shrewd manner using optimization methods to calculate a rejection probability
and to update the system. This method should allow an efficient study of the
dynamics of two-dimensional solids at high density.
